Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

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

Jasso, Gustavo LU (2024) In Comptes Rendus Mathematique 362. p.1449-1453
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∞-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.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
A∞-algebras, Nakayama algebras, simple modules, Yoneda algebras
in
Comptes Rendus Mathematique
volume
362
pages
5 pages
publisher
Academie des sciences
external identifiers
  • scopus:85209710492
ISSN
1631-073X
DOI
10.5802/crmath.655
language
English
LU publication?
yes
id
f2a28bc4-966c-4075-8314-477e09e13e0d
date added to LUP
2025-02-17 10:14:24
date last changed
2025-04-04 14:54:40
@article{f2a28bc4-966c-4075-8314-477e09e13e0d,
  abstract     = {{<p>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∞-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.</p>}},
  author       = {{Jasso, Gustavo}},
  issn         = {{1631-073X}},
  keywords     = {{A∞-algebras; Nakayama algebras; simple modules; Yoneda algebras}},
  language     = {{eng}},
  pages        = {{1449--1453}},
  publisher    = {{Academie des sciences}},
  series       = {{Comptes Rendus Mathematique}},
  title        = {{On a theorem of B. Keller on Yoneda algebras of simple modules}},
  url          = {{http://dx.doi.org/10.5802/crmath.655}},
  doi          = {{10.5802/crmath.655}},
  volume       = {{362}},
  year         = {{2024}},
}