On the Lie algebra structure of integrable derivations
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Accepted version
Author(s)
Briggs, Benjamin
Rubio y Degrassi, Lleonard
Type
Journal Article
Abstract
Building on work of Gerstenhaber, we show that the space of integrable derivations on an Artin algebra A forms a Lie algebra, and a restricted
Lie algebra if A contains a field of characteristic p. We deduce that the space
of integrable classes in HH1
(A) 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.
Lie algebra if A contains a field of characteristic p. We deduce that the space
of integrable classes in HH1
(A) 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.
Date Issued
2023-12
Date Acceptance
2023-05-19
Citation
Bulletin of the London Mathematical Society, 2023, 55 (6), pp.2617-2634
ISSN
0024-6093
Publisher
Wiley
Start Page
2617
End Page
2634
Journal / Book Title
Bulletin of the London Mathematical Society
Volume
55
Issue
6
Copyright Statement
Copyright © 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. This is the peer reviewed version of the following article: Briggs, B. and Rubio y Degrassi, L. (2023), On the Lie algebra structure of integrable derivations. Bull. London Math. Soc., 55: 2617-2634., which has been published in final form at https://doi.org/10.1112/blms.12884. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
Identifier
http://dx.doi.org/10.1112/blms.12884
Publication Status
Published
Date Publish Online
2023-07-06