Journal of Pure and Applied Algebra最新文献

{"title":"Amplitudes in persistence theory","authors":"Barbara Giunti ,&nbsp;John S. Nolan ,&nbsp;Nina Otter ,&nbsp;Lukas Waas","doi":"10.1016/j.jpaa.2024.107770","DOIUrl":"10.1016/j.jpaa.2024.107770","url":null,"abstract":"<div><p>The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants that one associates with data sets. Here we introduce a general framework to compare distances and invariants in multiparameter persistence, where there is no natural choice of invariants and distances between them. We define amplitudes, monotone, and subadditive invariants that arise from assigning a non-negative real number to objects of an abelian category. We then present different ways to associate distances to such invariants, and we provide a classification of classes of amplitudes relevant to topological data analysis. In addition, we study the relationships as well as the discriminative power of such amplitude distances arising in topological data analysis scenarios.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001671/pdfft?md5=13447f7bb8eeb6603f17dd7471b6786f&pid=1-s2.0-S0022404924001671-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Central products and the Chermak–Delgado lattice","authors":"William Cocke ,&nbsp;Ryan McCulloch","doi":"10.1016/j.jpaa.2024.107769","DOIUrl":"https://doi.org/10.1016/j.jpaa.2024.107769","url":null,"abstract":"<div><p>The Chermak–Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups. We prove that the Chermak–Delgado lattice of a central product contains the product of the Chermak–Delgado lattices of the relevant central factors. Furthermore, we obtain information about heights of elements in the Chermak–Delgado lattice relative to their heights in the Chermak–Delgado lattices of central factors. We also explore how the central product can be used as a tool in investigating Chermak–Delgado lattices.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002240492400166X/pdfft?md5=b017909bfa3dc92b57a4f28346dc47fa&pid=1-s2.0-S002240492400166X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141593081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hecke algebras and edge contractions","authors":"Yiqiang Li","doi":"10.1016/j.jpaa.2024.107768","DOIUrl":"10.1016/j.jpaa.2024.107768","url":null,"abstract":"<div><p>We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the order types of hammocks for domestic string algebras","authors":"Shantanu Sardar,&nbsp;Amit Kuber","doi":"10.1016/j.jpaa.2024.107763","DOIUrl":"https://doi.org/10.1016/j.jpaa.2024.107763","url":null,"abstract":"<div><p>In the representation-theoretic study of finite dimensional associative algebras over an algebraically closed field, Brenner introduced certain partially ordered sets known as <em>hammocks</em> to encode factorizations of maps between indecomposable finitely generated modules. In the context of domestic string algebras, Schröer introduced a simpler version of hammocks in his doctoral thesis that are bounded discrete linear orders. In this paper, we characterize the class of order types(=order isomorphism classes) of hammock linear orders for domestic string algebras as the bounded discrete ones amongst the class <span><math><mi>L</mi><msub><mrow><mi>O</mi></mrow><mrow><mi>fp</mi></mrow></msub></math></span> of <em>finitely presented linear orders</em>–the smallest class of linear orders containing finite linear orders as well as <em>ω</em>, and that is closed under isomorphisms, order reversal, finite order sums and antilexicographic products.</p><p>In fact, we provide a multi-step algorithm to compute the order type of any closed interval in the hammock, and prove the correctness of this algorithm. A major step of this algorithm is the construction of a variation, which we call the <em>arch bridge quiver</em>, of a finite combinatorial gadget called the <em>bridge quiver</em> introduced by Schröer. He utilised the graph-theoretic properties of the bridge quiver for the computation of some representation-theoretic numerical invariants of domestic string algebras. The vertices of the bridge quiver are (representatives of cyclic permutations of) bands and its arrows are certain band-free strings. There is a natural but ill-behaved partial binary operation, ∘, on a superset of the set of bridges consisting of <em>weak bridges</em> such that bridges are precisely the ∘-irreducibles. We equip an even larger yet finite set of <em>weak arch bridges</em> with another partial binary operation, <span><math><msub><mrow><mo>∘</mo></mrow><mrow><mi>H</mi></mrow></msub></math></span>, to obtain a finite category. The binary operation <span><math><msub><mrow><mo>∘</mo></mrow><mrow><mi>H</mi></mrow></msub></math></span> uses isomorphisms between hammocks and explicitly relies on the description of the domestic string algebra as a bound quiver algebra. Each weak arch bridge admits a unique <span><math><msub><mrow><mo>∘</mo></mrow><mrow><mi>H</mi></mrow></msub></math></span>-factorization into <em>arch bridges</em>, i.e., the <span><math><msub><mrow><mo>∘</mo></mrow><mrow><mi>H</mi></mrow></msub></math></span>-irreducibles.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141593080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some special coprime actions and their consequences","authors":"Gülı̇n Ercan ,&nbsp;İsmaı̇l Ş. Güloğlu ,&nbsp;M. Yası̇r Kizmaz ,&nbsp;Danila O. Revin","doi":"10.1016/j.jpaa.2024.107764","DOIUrl":"https://doi.org/10.1016/j.jpaa.2024.107764","url":null,"abstract":"<div><p>Let a group <em>A</em> act on the group <em>G</em> coprimely. Suppose that the order of the fixed point subgroup <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is not divisible by an arbitrary but fixed prime <em>p</em>. In the present paper we determine bounds for the <em>p</em>-length of the group <em>G</em> in terms of the order of <em>A</em>, and investigate how some <em>A</em>-invariant <em>p</em>-subgroups are embedded in <em>G</em> under various additional assumptions.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141606410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nil graded algebras associated to triangular matrices and their applications to Soergel calculus","authors":"","doi":"10.1016/j.jpaa.2024.107766","DOIUrl":"10.1016/j.jpaa.2024.107766","url":null,"abstract":"<div><p>We introduce and study a category of algebras strongly connected with the structure of the Gelfand-Tsetlin subalgebras of the endomorphism algebras of Bott-Samelson bimodules. We develop a series of techniques that allow us to obtain optimal presentations for the many Gelfand-Tsetlin subalgebras appearing in the context of the Diagrammatic Soergel Category.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Representations of the cyclotomic oriented Brauer-Clifford supercategory","authors":"Mengmeng Gao,&nbsp;Hebing Rui,&nbsp;Linliang Song","doi":"10.1016/j.jpaa.2024.107767","DOIUrl":"10.1016/j.jpaa.2024.107767","url":null,"abstract":"<div><p>Let <span><math><mi>k</mi></math></span> be an algebraically closed field with characteristic <em>p</em> different from 2. We generalize the notion of a weakly triangular decomposition in <span>[7]</span> to the super case called a super weakly triangular decomposition. We show that the underlying even category of locally finite-dimensional left <em>A</em>-supermodules is an upper finite fully stratified category in the sense of <span>[6, Definition 3.34]</span> if the superalgebra <em>A</em> admits an upper finite super weakly triangular decomposition. In particular, when <em>A</em> is the locally unital superalgebra associated with the cyclotomic oriented Brauer-Clifford supercategory in <span>[1]</span>, the Grothendieck group of the category of left <em>A</em>-supermodules admitting finite standard flags has a <span><math><mi>g</mi></math></span>-module structure that is isomorphic to the tensor product of an integrable lowest weight and an integrable highest weight <span><math><mi>g</mi></math></span>-module, where <span><math><mi>g</mi></math></span> is the complex Kac-Moody Lie algebra of type <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mn>2</mn><mi>ℓ</mi></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span> (resp., <span><math><msub><mrow><mi>B</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>) if <span><math><mi>p</mi><mo>=</mo><mn>2</mn><mi>ℓ</mi><mo>+</mo><mn>1</mn></math></span> (resp., <span><math><mi>p</mi><mo>=</mo><mn>0</mn></math></span>).</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Marked Godeaux surfaces with special bicanonical fibers","authors":"Frank-Olaf Schreyer ,&nbsp;Isabel Stenger","doi":"10.1016/j.jpaa.2024.107765","DOIUrl":"10.1016/j.jpaa.2024.107765","url":null,"abstract":"<div><p>In this paper we study marked numerical Godeaux surfaces with special bicanonical fibers. Based on the construction method of marked Godeaux surfaces in <span>[12]</span> we give a complete characterization for the existence of hyperelliptic bicanonical fibers and torsion fibers. Moreover, we describe how the families of Reid and Miyaoka with torsion <span><math><mi>Z</mi><mo>/</mo><mn>3</mn><mi>Z</mi></math></span> and <span><math><mi>Z</mi><mo>/</mo><mn>5</mn><mi>Z</mi></math></span> arise in our homological setting.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001622/pdfft?md5=24a063a7a56ffe64e021631c53abdb1f&pid=1-s2.0-S0022404924001622-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sums of squares in function fields over henselian discretely valued fields","authors":"Gonzalo Manzano-Flores","doi":"10.1016/j.jpaa.2024.107756","DOIUrl":"https://doi.org/10.1016/j.jpaa.2024.107756","url":null,"abstract":"<div><p>Let <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> and let <em>K</em> be a field with a henselian discrete valuation of rank <em>n</em> with hereditarily euclidean residue field. Let <span><math><mi>F</mi><mo>/</mo><mi>K</mi></math></span> be a function field in one variable. It is known that every sum of squares is a sum of 3 squares. We determine the order of the group of nonzero sums of 3 squares modulo sums of 2 squares in <em>F</em> in terms of equivalence classes of certain discrete valuations of <em>F</em> of rank at most <em>n</em>. In the case of function fields of hyperelliptic curves of genus <em>g</em>, K.J. Becher and J. Van Geel showed that the order of this quotient group is bounded by <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi><mo>(</mo><mi>g</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>. We show that this bound is optimal. Moreover, in the case where <span><math><mi>n</mi><mo>=</mo><mn>1</mn></math></span>, we show that if <span><math><mi>F</mi><mo>/</mo><mi>K</mi></math></span> is a hyperelliptic function field such that the order of this quotient group is <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>, then <em>F</em> is nonreal.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak Z-structures for some combinatorial group constructions","authors":"M. Cárdenas,&nbsp;F.F. Lasheras,&nbsp;A. Quintero","doi":"10.1016/j.jpaa.2024.107761","DOIUrl":"10.1016/j.jpaa.2024.107761","url":null,"abstract":"<div><p>Bestvina <span>[1]</span> introduced the notion of a (weak) <span><math><mi>Z</mi></math></span>-structure and (weak) <span><math><mi>Z</mi></math></span>-boundary for a torsion-free group, motivated by the notion of boundary for hyperbolic and <span><math><mi>C</mi><mi>A</mi><mi>T</mi><mo>(</mo><mn>0</mn><mo>)</mo></math></span> groups. Since then, some classes of groups have been shown to admit a (weak) <span><math><mi>Z</mi></math></span>-structure (see <span>[5]</span>, <span>[20]</span>, <span>[22]</span> for example); in fact, in all cases these groups are semistable at infinity and happen to have a pro-(finitely generated free) fundamental pro-group. The question whether or not every type <span><math><mi>F</mi></math></span> group admits such a structure remains open. In <span>[33]</span> it was shown that the property of admitting such a structure is closed under direct products and free products. Our main results are as follows.</p><p>THEOREM: Let <em>G</em> be a torsion-free and semistable at infinity finitely presented group with a pro-(finitely generated free) fundamental pro-group at each end. If <em>G</em> has a finite graph of groups decomposition in which all the groups involved are of type <span><math><mi>F</mi></math></span> and inward tame (in particular, if they all admit a weak <span><math><mi>Z</mi></math></span>-structure) then <em>G</em> admits a weak <span><math><mi>Z</mi></math></span>-structure.</p><p>COROLLARY: The class of those 1-ended and semistable at infinity torsion-free finitely presented groups which admit a weak <span><math><mi>Z</mi></math></span>-structure and have a pro-(finitely generated free) fundamental pro-group is closed under amalgamated products (resp. HNN-extensions) over finitely generated free groups.</p><p>On the other hand, given a finitely presented group <em>G</em> and a monomorphism <span><math><mi>φ</mi><mo>:</mo><mi>G</mi><mo>⟶</mo><mi>G</mi></math></span>, we may consider the ascending HNN-extension <span><math><mi>G</mi><msub><mrow><mo>⁎</mo></mrow><mrow><mi>φ</mi></mrow></msub><mo>=</mo><mo>〈</mo><mi>G</mi><mo>,</mo><mi>t</mi><mspace></mspace><mo>;</mo><mspace></mspace><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>g</mi><mi>t</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>g</mi><mo>)</mo><mo>,</mo><mi>g</mi><mo>∈</mo><mi>G</mi><mo>〉</mo></math></span>. The results in <span>[26]</span> together with the Theorem above yield the following:</p><p>PROPOSITION: If a finitely presented torsion-free group <em>G</em> is of type <span><math><mi>F</mi></math></span> and inward tame, then any (1-ended) ascending HNN-extension <span><math><mi>G</mi><msub><mrow><mo>⁎</mo></mrow><mrow><mi>φ</mi></mrow></msub></math></span> admits a weak <span><math><mi>Z</mi></math></span>-structure.</p><p>In the particular case <span><math><mi>φ</mi><mo>∈</mo><mi>A</mi><mi>u</mi><mi>t</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, this ascending HNN-extension corresponds to a semidirect p","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}