On the Lie algebra structure of integrable derivations
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On the Lie algebra structure of integrable derivations. / Briggs, Benjamin; Rubio y Degrassi, Lleonard.
In: Bulletin of the London Mathematical Society, Vol. 55, No. 6, 2023, p. 2617-2634.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On the Lie algebra structure of integrable derivations
AU - Briggs, Benjamin
AU - Rubio y Degrassi, Lleonard
N1 - Publisher Copyright: © 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85164460487&partnerID=8YFLogxK
U2 - 10.1112/blms.12884
DO - 10.1112/blms.12884
M3 - Journal article
AN - SCOPUS:85164460487
VL - 55
SP - 2617
EP - 2634
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
IS - 6
ER -
ID: 360263518