A∞-coderivations and the Gerstenhaber bracket on Hochschild cohomology

被引：3

作者：

Negron, Cris ^{[1
]}

Volkov, Yury ^{[2
]}

Witherspoon, Sarah ^{[3
]}

机构：

[1] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

[2] St Petersburg State Univ, Dept Math & Mech, St Petersburg 199034, Russia

[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2020年 / 14卷 / 02期

关键词：

Hochschild cohomology; Gerstenhaber bracket; A(infinity)-coalgebras; A(infinity)-coderivations; LIE BRACKET;

D O I：

10.4171/JNCG/372

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：531 / 565

页数：35

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