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On the Lie algebra structure of integrable derivations.
- Source :
-
Bulletin of the London Mathematical Society . Dec2023, Vol. 55 Issue 6, p2617-2634. 18p. - Publication Year :
- 2023
-
Abstract
- Building on work of Gerstenhaber, we show that the space of integrable derivations on an Artin algebra A$A$ forms a Lie algebra, and a restricted Lie algebra if A$A$ contains a field of characteristic p$p$. We deduce that the space of integrable classes in HH1(A)${\operatorname{HH}}^1(A)$ forms a (restricted) Lie algebra that is invariant under derived equivalences, and under stable equivalences of Morita type between selfâinjective algebras. We also provide negative answers to questions about integrable derivations posed by Linckelmann and by Farkas, Geiss and Marcos. Along the way, we compute the first Hochschild cohomology of the group algebra of any symmetric group. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIE algebras
*GROUP algebras
*COHOMOLOGY theory
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00246093
- Volume :
- 55
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Bulletin of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 174107258
- Full Text :
- https://doi.org/10.1112/blms.12884