A(infinity)-coderivations and the Gerstenhaber bracket on Hochschild cohomology

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A(infinity)-coderivations and the Gerstenhaber bracket on Hochschild cohomology. / Negron, Cris; Volkov, Yury; Witherspoon, Sarah.

In: Journal of Noncommutative Geometry, Vol. 14, No. 2, 2020, p. 531-565.

Research output: Contribution to journal › Article › peer-review

Author

Negron, Cris ; Volkov, Yury ; Witherspoon, Sarah. / A(infinity)-coderivations and the Gerstenhaber bracket on Hochschild cohomology. In: Journal of Noncommutative Geometry. 2020 ; Vol. 14, No. 2. pp. 531-565.

BibTeX

@article{564bcfb7157a437f9a37d5986a59cffc,

title = "A(infinity)-coderivations and the Gerstenhaber bracket on Hochschild cohomology",

abstract = "We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber bracket is the graded commutator of infinity coderivations. We thus generalize, to an arbitrary resolution, Stasheff's realization of the Gerstenhaber bracket on Hochschild cohomology as the graded commutator of coderivations on the tensor coalgebra of the algebra.",

keywords = "Hochschild cohomology, Gerstenhaber bracket, A(infinity)-coalgebras, A(infinity)-coderivations, LIE BRACKET, A -coalgebras-coderivations -coderivations, A1-coalgebras-coderivations1-coderivations",

author = "Cris Negron and Yury Volkov and Sarah Witherspoon",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society",

year = "2020",

doi = "10.4171/JNCG/372",

language = "English",

volume = "14",

pages = "531--565",

journal = "Journal of Noncommutative Geometry",

issn = "1661-6952",

publisher = "European Mathematical Society Publishing House",

number = "2",

}

RIS

TY - JOUR

T1 - A(infinity)-coderivations and the Gerstenhaber bracket on Hochschild cohomology

AU - Negron, Cris

AU - Volkov, Yury

AU - Witherspoon, Sarah

N1 - Publisher Copyright: © European Mathematical Society

PY - 2020

Y1 - 2020

N2 - We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber bracket is the graded commutator of infinity coderivations. We thus generalize, to an arbitrary resolution, Stasheff's realization of the Gerstenhaber bracket on Hochschild cohomology as the graded commutator of coderivations on the tensor coalgebra of the algebra.

AB - We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber bracket is the graded commutator of infinity coderivations. We thus generalize, to an arbitrary resolution, Stasheff's realization of the Gerstenhaber bracket on Hochschild cohomology as the graded commutator of coderivations on the tensor coalgebra of the algebra.

KW - Hochschild cohomology

KW - Gerstenhaber bracket

KW - A(infinity)-coalgebras

KW - A(infinity)-coderivations

KW - LIE BRACKET

KW - A -coalgebras-coderivations -coderivations

KW - A1-coalgebras-coderivations1-coderivations

UR - http://www.scopus.com/inward/record.url?scp=85091664757&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4e81cfd6-7650-30ba-89a5-d068f1384bda/

U2 - 10.4171/JNCG/372

DO - 10.4171/JNCG/372

M3 - Article

VL - 14

SP - 531

EP - 565

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 2

ER -

ID: 62213123