Stable invariance of the restricted Lie algebra structure of Hochschild cohomology

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Stable invariance of the restricted Lie algebra structure of Hochschild cohomology. / Briggs, Benjamin; Degrassi, Lleonard Rubio Y.

In: Pacific Journal of Mathematics, Vol. 321, No. 1, 2022, p. 45-73.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Briggs, B & Degrassi, LRY 2022, 'Stable invariance of the restricted Lie algebra structure of Hochschild cohomology', Pacific Journal of Mathematics, vol. 321, no. 1, pp. 45-73. https://doi.org/10.2140/pjm.2022.321.45

APA

Briggs, B., & Degrassi, L. R. Y. (2022). Stable invariance of the restricted Lie algebra structure of Hochschild cohomology. Pacific Journal of Mathematics, 321(1), 45-73. https://doi.org/10.2140/pjm.2022.321.45

Vancouver

Briggs B, Degrassi LRY. Stable invariance of the restricted Lie algebra structure of Hochschild cohomology. Pacific Journal of Mathematics. 2022;321(1):45-73. https://doi.org/10.2140/pjm.2022.321.45

Author

Briggs, Benjamin ; Degrassi, Lleonard Rubio Y. / Stable invariance of the restricted Lie algebra structure of Hochschild cohomology. In: Pacific Journal of Mathematics. 2022 ; Vol. 321, No. 1. pp. 45-73.

Bibtex

@article{51819edb6bc548dc99c991f6f77561cc,
title = "Stable invariance of the restricted Lie algebra structure of Hochschild cohomology",
abstract = "We show that the restricted Lie algebra structure on Hochschild cohomology is invariant under stable equivalences of Morita type between self-injective algebras. Thereby, we obtain a number of positive characteristic stable invariants, such as the p-toral rank of HH1(A, A). We also prove a more general result concerning Iwanaga–Gorenstein algebras, using a generalization of stable equivalences of Morita type. Several applications are given to commutative algebra and modular representation theory.",
keywords = "B-infinity algebra, Gerstenhaber bracket, Hochschild cohomology, restricted Lie algebra, singularity category, stable equivalence of Morita type",
author = "Benjamin Briggs and Degrassi, {Lleonard Rubio Y.}",
note = "Publisher Copyright: {\textcopyright} 2022 Mathematical Sciences Publishers",
year = "2022",
doi = "10.2140/pjm.2022.321.45",
language = "English",
volume = "321",
pages = "45--73",
journal = "Pacific Journal of Mathematics",
issn = "0030-8730",
publisher = "Mathematical Sciences Publishers",
number = "1",

}

RIS

TY - JOUR

T1 - Stable invariance of the restricted Lie algebra structure of Hochschild cohomology

AU - Briggs, Benjamin

AU - Degrassi, Lleonard Rubio Y.

N1 - Publisher Copyright: © 2022 Mathematical Sciences Publishers

PY - 2022

Y1 - 2022

N2 - We show that the restricted Lie algebra structure on Hochschild cohomology is invariant under stable equivalences of Morita type between self-injective algebras. Thereby, we obtain a number of positive characteristic stable invariants, such as the p-toral rank of HH1(A, A). We also prove a more general result concerning Iwanaga–Gorenstein algebras, using a generalization of stable equivalences of Morita type. Several applications are given to commutative algebra and modular representation theory.

AB - We show that the restricted Lie algebra structure on Hochschild cohomology is invariant under stable equivalences of Morita type between self-injective algebras. Thereby, we obtain a number of positive characteristic stable invariants, such as the p-toral rank of HH1(A, A). We also prove a more general result concerning Iwanaga–Gorenstein algebras, using a generalization of stable equivalences of Morita type. Several applications are given to commutative algebra and modular representation theory.

KW - B-infinity algebra

KW - Gerstenhaber bracket

KW - Hochschild cohomology

KW - restricted Lie algebra

KW - singularity category

KW - stable equivalence of Morita type

U2 - 10.2140/pjm.2022.321.45

DO - 10.2140/pjm.2022.321.45

M3 - Journal article

AN - SCOPUS:85143116038

VL - 321

SP - 45

EP - 73

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -

ID: 342967985