$A_{\infty}$-coderivations and the Gerstenhaber bracket on Hochschild cohomology
| Autor: | Cris Negron, Yury Volkov, Sarah Witherspoon |
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| Rok vydání: | 2020 |
| Předmět: |
Commutator
Pure mathematics Algebra and Number Theory Mathematics::Rings and Algebras Mathematics - Rings and Algebras 16. Peace & justice Mathematics::Algebraic Topology Cohomology Bracket (mathematics) Rings and Algebras (math.RA) Mathematics::K-Theory and Homology Mathematics::Category Theory Mathematics::Quantum Algebra Tensor (intrinsic definition) Lie algebra FOS: Mathematics Bimodule Geometry and Topology Representation Theory (math.RT) Algebra over a field Mathematics - Representation Theory Mathematical Physics Mathematics Resolution (algebra) |
| Zdroj: | Journal of Noncommutative Geometry. 14:531-565 |
| ISSN: | 1661-6952 |
| DOI: | 10.4171/jncg/372 |
| Popis: | 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. Comment: 26 pages; updated references |
| Databáze: | OpenAIRE |
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