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

Harvard

Briggs, B & Rubio y Degrassi, L 2023, 'On the Lie algebra structure of integrable derivations', Bulletin of the London Mathematical Society, vol. 55, no. 6, pp. 2617-2634. https://doi.org/10.1112/blms.12884

APA

Briggs, B., & Rubio y Degrassi, L. (2023). On the Lie algebra structure of integrable derivations. Bulletin of the London Mathematical Society, 55(6), 2617-2634. https://doi.org/10.1112/blms.12884

Vancouver

Briggs B, Rubio y Degrassi L. On the Lie algebra structure of integrable derivations. Bulletin of the London Mathematical Society. 2023;55(6):2617-2634. https://doi.org/10.1112/blms.12884

Author

Briggs, Benjamin ; Rubio y Degrassi, Lleonard. / On the Lie algebra structure of integrable derivations. In: Bulletin of the London Mathematical Society. 2023 ; Vol. 55, No. 6. pp. 2617-2634.

Bibtex

@article{9c7038f071cb455a892e0129b432256d,
title = "On the Lie algebra structure of integrable derivations",
abstract = "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.",
author = "Benjamin Briggs and {Rubio y Degrassi}, Lleonard",
note = "Publisher Copyright: {\textcopyright} 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",
year = "2023",
doi = "10.1112/blms.12884",
language = "English",
volume = "55",
pages = "2617--2634",
journal = "Bulletin of the London Mathematical Society",
issn = "0024-6093",
publisher = "Oxford University Press",
number = "6",

}

RIS

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