Journal of the Australian Mathematical Society最新文献

{"title":"JAZ volume 113 issue 1 Cover and Back matter","authors":"","doi":"10.1017/s144678872100032x","DOIUrl":"https://doi.org/10.1017/s144678872100032x","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79528322","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":"JAZ volume 113 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s1446788721000318","DOIUrl":"https://doi.org/10.1017/s1446788721000318","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72793738","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":"SEMIRING AND INVOLUTION IDENTITIES OF POWER GROUPS","authors":"S. V. Gusev, Mikhail Volkov","doi":"10.1017/S1446788722000374","DOIUrl":"https://doi.org/10.1017/S1446788722000374","url":null,"abstract":"\u0000\t <jats:p>For every group <jats:italic>G</jats:italic>, the set <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=\"S1446788722000374_inline1.png\" />\u0000\t\t<jats:tex-math>\u0000$mathcal {P}(G)$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> of its subsets forms a semiring under set-theoretical union <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=\"S1446788722000374_inline2.png\" />\u0000\t\t<jats:tex-math>\u0000$cup $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> and element-wise multiplication <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788722000374_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$cdot $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>, and forms an involution semigroup under <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788722000374_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$cdot $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> and element-wise inversion <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788722000374_inline5.png\" />\u0000\t\t<jats:tex-math>\u0000${}^{-1}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>. We show that if the group <jats:italic>G</jats:italic> is finite, non-Dedekind, and solvable, neither the semiring <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788722000374_inline6.png\" />\u0000\t\t<jats:tex-math>\u0000$(mathcal {P}(G),cup ,cdot )$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> nor the involution semigroup <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788722000374_inline7.png\" />\u0000\t\t<jats:tex-math>\u0000$(mathcal {P}(G),cdot ,{}^{-1})$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> admits a finite identity basis. We also solve the finite basis problem for the semiring of Hall relations over any finite set.</jats:p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84842984","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":"REGULARITY OF AML FUNCTIONS IN TWO-DIMENSIONAL NORMED SPACES","authors":"Sebastián Tapia-García","doi":"10.1017/S1446788722000088","DOIUrl":"https://doi.org/10.1017/S1446788722000088","url":null,"abstract":"Abstract Savin [‘ \u0000$mathcal {C}^{1}$\u0000 regularity for infinity harmonic functions in two dimensions’, Arch. Ration. Mech. Anal. 3(176) (2005), 351–361] proved that every planar absolutely minimizing Lipschitz (AML) function is continuously differentiable whenever the ambient space is Euclidean. More recently, Peng et al. [‘Regularity of absolute minimizers for continuous convex Hamiltonians’, J. Differential Equations 274 (2021), 1115–1164] proved that this property remains true for planar AML functions for certain convex Hamiltonians, using some Euclidean techniques. Their result can be applied to AML functions defined in two-dimensional normed spaces with differentiable norm. In this work we develop a purely non-Euclidean technique to obtain the regularity of planar AML functions in two-dimensional normed spaces with differentiable norm.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78210187","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":"LEAVITT PATH ALGEBRAS OF WEIGHTED AND SEPARATED GRAPHS","authors":"P. Ara","doi":"10.1017/S1446788722000155","DOIUrl":"https://doi.org/10.1017/S1446788722000155","url":null,"abstract":"Abstract In this paper, we show that Leavitt path algebras of weighted graphs and Leavitt path algebras of separated graphs are intimately related. We prove that any Leavitt path algebra \u0000$L(E,omega )$\u0000 of a row-finite vertex weighted graph \u0000$(E,omega )$\u0000 is \u0000$*$\u0000 -isomorphic to the lower Leavitt path algebra of a certain bipartite separated graph \u0000$(E(omega ),C(omega ))$\u0000 . For a general locally finite weighted graph \u0000$(E, omega )$\u0000 , we show that a certain quotient \u0000$L_1(E,omega )$\u0000 of \u0000$L(E,omega )$\u0000 is \u0000$*$\u0000 -isomorphic to an upper Leavitt path algebra of another bipartite separated graph \u0000$(E(w)_1,C(w)^1)$\u0000 . We furthermore introduce the algebra \u0000${L^{mathrm {ab}}} (E,w)$\u0000 , which is a universal tame \u0000$*$\u0000 -algebra generated by a set of partial isometries. We draw some consequences of our results for the structure of ideals of \u0000$L(E,omega )$\u0000 , and we study in detail two different maximal ideals of the Leavitt algebra \u0000$L(m,n)$\u0000 .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85186930","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":"RATIONAL -STABILITY OF CONTINUOUS -ALGEBRAS","authors":"Apurva Seth, P. Vaidyanathan","doi":"10.1017/s144678872200009x","DOIUrl":"https://doi.org/10.1017/s144678872200009x","url":null,"abstract":"\u0000 We show that the properties of being rationally K-stable passes from the fibres of a continuous \u0000 \u0000 \u0000 \u0000$C(X)$\u0000\u0000 \u0000 -algebra to the ambient algebra, under the assumption that the underlying space X is compact, metrizable, and of finite covering dimension. As an application, we show that a crossed product C*-algebra is (rationally) K-stable provided the underlying C*-algebra is (rationally) K-stable, and the action has finite Rokhlin dimension with commuting towers.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78369372","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":"JAZ volume 112 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s144678872100029x","DOIUrl":"https://doi.org/10.1017/s144678872100029x","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83440036","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":"INDEX","authors":"","doi":"10.1017/s1446788721000306","DOIUrl":"https://doi.org/10.1017/s1446788721000306","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80100733","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":"JAZ volume 112 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1446788721000288","DOIUrl":"https://doi.org/10.1017/s1446788721000288","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80548847","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":"MULTIPLICATION TABLES AND WORD-HYPERBOLICITY IN FREE PRODUCTS OF SEMIGROUPS, MONOIDS AND GROUPS","authors":"Carl-Fredrik Nyberg Brodda","doi":"10.1017/s1446788723000010","DOIUrl":"https://doi.org/10.1017/s1446788723000010","url":null,"abstract":"\u0000 This article studies the properties of word-hyperbolic semigroups and monoids, that is, those having context-free multiplication tables with respect to a regular combing, as defined by Duncan and Gilman [‘Word hyperbolic semigroups’, Math. Proc. Cambridge Philos. Soc.136(3) (2004), 513–524]. In particular, the preservation of word-hyperbolicity under taking free products is considered. Under mild conditions on the semigroups involved, satisfied, for example, by monoids or regular semigroups, we prove that the semigroup free product of two word-hyperbolic semigroups is again word-hyperbolic. Analogously, with a mild condition on the uniqueness of representation for the identity element, satisfied, for example, by groups, we prove that the monoid free product of two word-hyperbolic monoids is word-hyperbolic. The methods are language-theoretically general, and apply equally well to semigroups, monoids or groups with a \u0000 \u0000 \u0000 \u0000$mathbf {C}$\u0000\u0000 \u0000 -multiplication table, where \u0000 \u0000 \u0000 \u0000$mathbf {C}$\u0000\u0000 \u0000 is any reversal-closed super-\u0000 \u0000 \u0000 \u0000$operatorname {mathrm {AFL}}$\u0000\u0000 \u0000 . In particular, we deduce that the free product of two groups with \u0000 \u0000 \u0000 \u0000$mathbf {ET0L}$\u0000\u0000 \u0000 with respect to indexed multiplication tables again has an \u0000 \u0000 \u0000 \u0000$mathbf {ET0L}$\u0000\u0000 \u0000 with respect to an indexed multiplication table.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89099491","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}