Glasgow Mathematical Journal最新文献

{"title":"Stereographic compactification and affine bi-Lipschitz homeomorphisms","authors":"Vincent Grandjean, Roger Oliveira","doi":"10.1017/s001708952400017x","DOIUrl":"https://doi.org/10.1017/s001708952400017x","url":null,"abstract":"\u0000\t <jats:p>Let <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline1.png\"/>\u0000\t\t<jats:tex-math>\u0000$sigma _q ,:,{{mathbb{R}}^q} to{textbf{S}}^qsetminus N_q$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> be the inverse of the stereographic projection with center the north pole <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline2.png\"/>\u0000\t\t<jats:tex-math>\u0000$N_q$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>. Let <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline3.png\"/>\u0000\t\t<jats:tex-math>\u0000$W_i$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> be a closed subset of <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline4.png\"/>\u0000\t\t<jats:tex-math>\u0000${mathbb{R}}^{q_i}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>, for <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline5.png\"/>\u0000\t\t<jats:tex-math>\u0000$i=1,2$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>. Let <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline6.png\"/>\u0000\t\t<jats:tex-math>\u0000$Phi ,:,W_1 to W_2$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> be a bi-Lipschitz homeomorphism. The main result states that the homeomorphism <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline7.png\"/>\u0000\t\t<jats:tex-math>\u0000$sigma _{q_2}circ Phi circ sigma _{q_1}^{-1}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> is a bi-Lipschitz homeomorphism, extending bi-Lipschitz-ly at <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline8.png\"/>\u0000\t\t<jats:tex-math>\u0000$N_{q_1}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> with value <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952400017X_inline9.png\"/>\u0000\t\t<jats:tex-math>\u0000$N_{q_2}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> whenever <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140971318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Girth Alternative for subgroups of","authors":"Azer Akhmedov","doi":"10.1017/s0017089524000181","DOIUrl":"https://doi.org/10.1017/s0017089524000181","url":null,"abstract":"We prove the <jats:italic>Girth Alternative</jats:italic> for finitely generated subgroups of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000181_inline2.png\"/> <jats:tex-math> $PL_o(I)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. We also prove that a finitely generated subgroup of <jats:italic>Homeo</jats:italic><jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000181_inline3.png\"/> <jats:tex-math> $_{+}(I)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> which is sufficiently rich with hyperbolic-like elements has infinite girth.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thinness of some hypergeometric groups in","authors":"Sandip Singh, Shashank Vikram Singh","doi":"10.1017/s0017089524000168","DOIUrl":"https://doi.org/10.1017/s0017089524000168","url":null,"abstract":"We show the thinness of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000168_inline2.png\"/> <jats:tex-math> $7$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000168_inline3.png\"/> <jats:tex-math> $40$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> hypergeometric groups having a maximally unipotent monodromy in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000168_inline4.png\"/> <jats:tex-math> $mathrm{Sp}(6)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140834195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simplicial volume of manifolds with amenable fundamental group at infinity","authors":"Giuseppe Bargagnati","doi":"10.1017/s0017089524000107","DOIUrl":"https://doi.org/10.1017/s0017089524000107","url":null,"abstract":"We show that for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000107_inline1.png\" /> <jats:tex-math> $n neq 1,4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, the simplicial volume of an inward tame triangulable open <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000107_inline2.png\" /> <jats:tex-math> $n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-manifold <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000107_inline3.png\" /> <jats:tex-math> $M$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with amenable fundamental group at infinity at each end is finite; moreover, we show that if also <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000107_inline4.png\" /> <jats:tex-math> $pi _1(M)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is amenable, then the simplicial volume of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000107_inline5.png\" /> <jats:tex-math> $M$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> vanishes. We show that the same result holds for finitely-many-ended triangulable manifolds which are simply connected at infinity.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140636483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Maximal subgroups of a family of iterated monodromy groups","authors":"Karthika Rajeev, Anitha Thillaisundaram","doi":"10.1017/s0017089524000120","DOIUrl":"https://doi.org/10.1017/s0017089524000120","url":null,"abstract":"The Basilica group is a well-known 2-generated weakly branch, but not branch, group acting on the binary rooted tree. Recently, a more general form of the Basilica group has been investigated by Petschick and Rajeev, which is an <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000120_inline1.png\" /> <jats:tex-math> $s$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-generated weakly branch, but not branch, group that acts on the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000120_inline2.png\" /> <jats:tex-math> $m$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic tree, for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000120_inline3.png\" /> <jats:tex-math> $s,mge 2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. A larger family of groups, which contains these generalised Basilica groups, is the family of iterated monodromy groups. With the new developments by Francoeur, the study of the existence of maximal subgroups of infinite index has been extended from branch groups to weakly branch groups. Here we show that a subfamily of iterated monodromy groups, which more closely resemble the generalised Basilica groups, have maximal subgroups only of finite index.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Twisted Blanchfield pairings and twisted signatures III: Applications","authors":"Maciej Borodzik, Anthony Conway, Wojciech Politarczyk","doi":"10.1017/s0017089524000077","DOIUrl":"https://doi.org/10.1017/s0017089524000077","url":null,"abstract":"This paper describes how to compute algorithmically certain twisted signature invariants of a knot <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000077_inline1.png\" /> <jats:tex-math> $K$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> using twisted Blanchfield forms. An illustration of the algorithm is implemented on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000077_inline2.png\" /> <jats:tex-math> $(2,q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-torus knots. Additionally, using satellite formulas for these invariants, we also show how to obstruct the sliceness of certain iterated torus knots.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on quantum K-theory of root constructions","authors":"Hsian-Hua Tseng","doi":"10.1017/s0017089524000089","DOIUrl":"https://doi.org/10.1017/s0017089524000089","url":null,"abstract":"We consider K-theoretic Gromov-Witten theory of root constructions. We calculate some genus <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000089_inline1.png\" /> <jats:tex-math> $0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> K-theoretic Gromov-Witten invariants of a root gerbe. We also obtain a K-theoretic relative/orbifold correspondence in genus <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000089_inline2.png\" /> <jats:tex-math> $0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On almost quotient Yamabe solitons","authors":"Willian Tokura, Marcelo Barboza, Elismar Batista, Priscila Kai","doi":"10.1017/s0017089524000119","DOIUrl":"https://doi.org/10.1017/s0017089524000119","url":null,"abstract":"In this paper, we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call almost quotient Yamabe solitons as they extend quite naturally those already called quotient Yamabe solitons. We present sufficient conditions for a compact almost quotient Yamabe soliton to be either trivial or isometric with an Euclidean sphere. We also characterize noncompact almost gradient quotient Yamabe solitons satisfying certain conditions on both its Ricci tensor and potential function.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Galois points and Cremona transformations","authors":"Ahmed Abouelsaad","doi":"10.1017/s0017089524000090","DOIUrl":"https://doi.org/10.1017/s0017089524000090","url":null,"abstract":"In this article, we study Galois points of plane curves and the extension of the corresponding Galois group to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000090_inline1.png\" /> <jats:tex-math> $mathrm{Bir}(mathbb{P}^2)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. We prove that if the Galois group has order at most <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000090_inline2.png\" /> <jats:tex-math> $3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, it always extends to a subgroup of the Jonquières group associated with the point <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000090_inline3.png\" /> <jats:tex-math> $P$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Conversely, with a degree of at least <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000090_inline4.png\" /> <jats:tex-math> $4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, we prove that it is false. We provide an example of a Galois extension whose Galois group is extendable to Cremona transformations but not to a group of de Jonquières maps with respect to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000090_inline5.png\" /> <jats:tex-math> $P$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In addition, we also give an example of a Galois extension whose Galois group cannot be extended to Cremona transformations.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Triangular matrix categories over quasi-hereditary categories","authors":"Rafael Francisco Ochoa De La Cruz, Martin Ortíz Morales, Valente Santiago Vargas","doi":"10.1017/s0017089524000053","DOIUrl":"https://doi.org/10.1017/s0017089524000053","url":null,"abstract":"In this paper, we prove that the lower triangular matrix category <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline1.png\" /> <jats:tex-math> $Lambda =left [ begin{smallmatrix} mathcal{T}&amp;0 M&amp;mathcal{U} end{smallmatrix} right ]$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline2.png\" /> <jats:tex-math> $mathcal{T}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline3.png\" /> <jats:tex-math> $mathcal{U}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> are <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline4.png\" /> <jats:tex-math> $textrm{Hom}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-finite, Krull–Schmidt <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline5.png\" /> <jats:tex-math> $K$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-quasi-hereditary categories and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline6.png\" /> <jats:tex-math> $M$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is an <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline7.png\" /> <jats:tex-math> $mathcal{U}otimes _K mathcal{T}^{op}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-module that satisfies suitable conditions, is quasi-hereditary. This result generalizes the work of B. Zhu in his study on triangular matrix algebras over quasi-hereditary algebras. Moreover, we obtain a characterization of the category of the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline8.png\" /> <jats:tex-math> $_Lambda Delta$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-filtered <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000053_inline9.png\" /> <jats:tex-math> $Lambda$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-modules.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}