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On a theorem of B. Keller on Yoneda algebras of simple modules

Gustavo Jasso

Abstract

A theorem of Keller states that the Yoneda algebra of the simple modules over a finite-dimensional algebra is generated in cohomological degrees $0$ and $1$ as a minimal $A_\infty$-algebra. We provide a proof of an extension of Keller's theorem to abelian length categories by reducing the problem to a particular class of Nakayama algebras, where the claim can be shown by direct computation.

On a theorem of B. Keller on Yoneda algebras of simple modules

Abstract

A theorem of Keller states that the Yoneda algebra of the simple modules over a finite-dimensional algebra is generated in cohomological degrees and as a minimal -algebra. We provide a proof of an extension of Keller's theorem to abelian length categories by reducing the problem to a particular class of Nakayama algebras, where the claim can be shown by direct computation.
Paper Structure (2 sections, 1 theorem, 16 equations)

This paper contains 2 sections, 1 theorem, 16 equations.

Table of Contents

  1. Acknowledgements
  2. Financial support

Key Result

theorem 1

Let $\mathcal{A}$ be a $\mathbf{k}$-linear abelian length category KV18 with only finitely many pairwise non-isomorphic simple objects, for example the category of finite-dimensional modules over a finite-dimensional algebra. Let $S_1,\dots,S_n$ be a complete set of representatives of the simple obj

Theorems & Definitions (5)

  • theorem : Keller
  • remark
  • remark
  • proof : Proof of the theorem
  • remark