Ext-Finite Modules for Weakly Symmetric Algebras With Radical Cube Zero

Erdmann, Karin

doi:10.1017/s1446788716000331

Cited by 3 publications

(2 citation statements)

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“…Another class of examples of algebras arising as trivial extensions of almost gentle algebras is given by symmetric algebras with radical cube zero, which have been extensively studied; see for example [4,12,13,18]. It follows from the results in this paper and in [18] that an algebra is a symmetric algebra with radical cube zero if and only if it is a trivial extension of an almost gentle algebra where the paths in the quiver of the almost gentle algebra are all of length at most one.…”

Section: Introductionmentioning

confidence: 99%

Almost Gentle Algebras and their Trivial Extensions

Green¹,

Schroll²

2018

Proceedings of the Edinburgh Mathematical Society

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In this paper we define almost gentle algebras. They are monomial special multiserial algebras generalizing gentle algebras. We show that the trivial extension of an almost gentle algebra by its minimal injective co-generator is a symmetric special multiserial algebra and hence a Brauer configuration algebra. Conversely, we show that any almost gentle algebra is an admissible cut of a unique Brauer configuration algebra and as a consequence, we obtain that every Brauer configuration algebra with multiplicity function identically one, is the trivial extension of an almost gentle algebra. We show that to every almost gentle algebra A is associated a hypergraph, and that this hypergraph induces the Brauer configuration of the trivial extension of A. Amongst other things, this gives a combinatorial criterion to decide when two almost gentle algebras have isomorphic trivial extensions.

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Section: Introductionmentioning

confidence: 99%

Almost Gentle Algebras and their Trivial Extensions

Green¹,

Schroll²

2018

Proceedings of the Edinburgh Mathematical Society

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“…The algebras studied by Schulz therefore do not satisfy (Fg). More generally, weakly symmetric algebra with radical cube zero were investigated in [11], [12]. The algebras in these papers which have criminals happen to be special biserial, therefore one may ask when a special biserial weakly symmetric algebra has criminals.…”

Section: Introductionmentioning

confidence: 99%

Algebras with non-periodic bounded modules

Erdmann

2017

Journal of Algebra

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We study weakly symmetric special biserial algebra of infinite representation type. We show that usually some socle deformation of such an algebra has non-periodic bounded modules. The exceptions are precisely the algebras whose Brauer graph is a tree with no multiple edges. If the algebra has a non-periodic bounded module then its Hochschild cohomology cannot satisfy the finite generation property (Fg) introduced in [10].

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