Results 11 to 20 of about 2,140 (101)
Schurian‐finiteness of blocks of type A$A$ Hecke algebras
Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2333-2376, December 2023., 2023 Abstract For any algebra A$A$ over an algebraically closed field F$\mathbb {F}$, we say that an A$A$‐module M$M$ is Schurian if EndA(M)≅F$\operatorname{End}_A(M) \cong \mathbb {F}$. We say that A$A$ is Schurian‐finite if there are only finitely many isomorphism classes of Schurian A$A$‐modules, and Schurian‐infinite otherwise. By work of Demonet, Iyama
Susumu Ariki, Sinéad Lyle, Liron Speyer
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Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors
Proceedings of the London Mathematical Society, Volume 127, Issue 3, Page 513-588, September 2023., 2023 Abstract We show that the mesh mutations are the minimal relations among the g${\bm{g}}$‐vectors with respect to any initial seed in any finite‐type cluster algebra. We then use this algebraic result to derive geometric properties of the g${\bm{g}}$‐vector fan: we show that the space of all its polytopal realizations is a simplicial cone, and we then ...
Arnau Padrol +3 more
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Tame hereditary path algebras and amenability
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1837-1856, August 2023., 2023 Abstract In this note we revisit the notion of amenable representation type introduced by Gábor Elek. We show that tame hereditary path algebras of quivers of extended Dynkin type over any field k$k$ are of amenable type. This verifies a conjecture of Elek, which draws similarities to the tame‐wild dichotomy, for another class of tame algebras. We also
Sebastian Eckert
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Tilting quivers for BB‐tilted algebras
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1994-2017, August 2023., 2023 Abstract Let Λ$\Lambda$ be a hereditary algebra, B0=EndΛ(T0)$B_0=\operatorname{End}_\Lambda (T_0)$ be a tilted algebra. We will construct tilting B0$B_0$‐modules from tilting Λ$\Lambda$‐modules and use this result to show how tilting quivers of BB‐tilted algebras can be obtained from those of Λ$\Lambda$.
Hongwei Peng
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PBW Basis of the Modified Ringel–Hall Algebra of Type An via Gröbner–Shirshov Basis
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 In the Ringel–Hall algebra of Dynkin type, the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Gröbner–Shirshov basis, and the set of the corresponding irreducible elements forms a PBW‐type basis of the Ringel–Hall algebra. The aim of this paper is to generalize this result to the modified Ringel–
Desheng Hu, Abdukadir Obul, Naihuan Jing
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Bijections of silting complexes and derived Picard groups
Journal of the London Mathematical Society, Volume 106, Issue 2, Page 1008-1060, September 2022., 2022 Abstract We introduce a method that produces a bijection between the posets silt−A$\textrm {{{\bf silt}}-}{A}$ and silt−B$\textrm {{{\bf silt}}-}{B}$ formed by the isomorphism classes of basic silting complexes over finite‐dimensional k$k$‐algebras A$A$ and B$B$, by lifting A$A$ and B$B$ to two k[[X]]$k[\![X]\!]$‐orders which are isomorphic as rings ...
Florian Eisele
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Decidability of theories of modules over tubular algebras
Proceedings of the London Mathematical Society, Volume 123, Issue 5, Page 460-497, November 2021., 2021 Abstract We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite‐dimensional algebra (over a suitably recursive field) is tame if and only if its common theory of modules is decidable (Prest ...
Lorna Gregory
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Specht modules in the Auslander–Reiten quiver
Journal of Algebra, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Danz, Susanne, Erdmann, Karin
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The Auslander-Reiten Quiver of a Simple Curve Singularity [PDF]
Transactions of the American Mathematical Society, 1986 With any simple curve singularity (plane, complex, affine-algebraic) of Dynkin-type Δ \Delta we associate the category of all finitely generated torsionfree modules over its complete local ring. For each of these module categories we calculate the Auslander-Reiten quiver. We suggest the construction of the “twisted quiver” of a quiver
Dieterich, Ernst, Wiedemann, Alfred
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Tilting theory via stable homotopy theory [PDF]
, 2015 We show that certain tilting results for quivers are formal consequences of stability, and as such are part of a formal calculus available in any abstract stable homotopy theory.
Groth, Moritz, Stovicek, Jan
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