On the Lie algebra structure of integrable derivations
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Building on work of Gerstenhaber, we show that the space of integrable derivations on an Artin algebra (Formula presented.) forms a Lie algebra, and a restricted Lie algebra if (Formula presented.) contains a field of characteristic (Formula presented.). We deduce that the space of integrable classes in (Formula presented.) forms a (restricted) Lie algebra that is invariant under derived equivalences, and under stable equivalences of Morita type between self-injective 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.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Bulletin of the London Mathematical Society |
| Vol/bind | 55 |
| Udgave nummer | 6 |
| Sider (fra-til) | 2617-2634 |
| ISSN | 0024-6093 |
| DOI | |
| Status | Udgivet - 2023 |
Bibliografisk note
Funding Information:
The authors would like to thank the referee for their useful comments and suggestions on the manuscript. During this work, the first author was hosted by the Mathematical Sciences Research Institute in Berkeley, California, supported by the National Science Foundation under Grant Number: 1928930. The second author has been partially supported by EPSRC Grant EP/L01078X/1 and the project PRIN 2017 ‐ Categories, Algebras: Ring‐Theoretical and Homological Approaches. He also acknowledges support from the project REDCOM: Reducing complexity in algebra, logic, combinatorics, financed by the programme Ricerca Scientifica di Eccellenza 2018 of the Fondazione Cariverona.
Publisher Copyright:
© 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
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