Hochschild and ordinary cohomology rings of small categories

Xu, Fei

doi:10.1016/j.aim.2008.07.014

Cited by 55 publications

(56 citation statements)

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“…There are examples, due to Fei Xu [24], of finite categories for which not even the quotient of the Hochschild cohomology by its nil-radical is finitely generated. In contrast, for finite inverse categories, the above theorem has the following consequence: Corollary 1.2.…”

Section: Introductionmentioning

confidence: 99%

On inverse categories and transfer in cohomology

Linckelmann

2012

Proceedings of the Edinburgh Mathematical Society

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Citation: Linckelmann, M. (2013). On inverse categories and transfer in cohomology.Proceedings of the Edinburgh Mathematical Society, 56(1), pp. 187-210. doi: 10.1017/S0013091512000211 This is the accepted version of the paper.This version of the publication may differ from the final published version. , extended to inverse categories, that finite inverse category algebras are isomorphic to their associated groupoid algebras; in particular, they are symmetric algebras with canonical symmetrising forms. We deduce the existence of transfer maps in cohomology and Hochschild cohomology from certain inverse subcategories. This is in part motivated by the observation that for certain categories C, being a Mackey functor on C is equivalent to being extendible to a suitable inverse category containing C. We show further that extensions of inverse categories by abelian groups are again inverse categories. Permanent

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Section: Introductionmentioning

confidence: 99%

On inverse categories and transfer in cohomology

Linckelmann

2012

Proceedings of the Edinburgh Mathematical Society

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“…Note that F (P), identified with a subposet of P e , is convex but not ideal in P e kP⋊G . see [11] for the latter isomorphism. Along with Boisen's result, our first statement gives rise to the second.…”

Section: Block Theorymentioning

confidence: 93%

“…Enveloping categories and diagonal categories. These constructions were used in [11]. Let C e = C × C op be the product category, between a small category C and its opposite, called the enveloping category.…”

Section: 2mentioning

confidence: 99%

Local representation theory of transporter categories

2018

Journal of Algebra

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We attempt to generalize the p-modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our tasks through modules of transporter category algebras, a type of Gorenstein skew group algebras. The Kan extensions, upgrading the induction and co-induction, are our main tools to establish connections between representations of a transporter category and of its transporter subcategories. Some important constructions and theorems in local representation theory of finite groups are generalized.

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“…Moreover, [16,17], and [20] make us consider whether we can give necessary and sufficient conditions on a finite dimensional algebra A for HH * A / to be finitely generated as an algebra (cf. [14,Introduction]).…”

Section: Introductionmentioning

confidence: 99%