$A_{\infty}$-coderivations and the Gerstenhaber bracket on Hochschild cohomology
Copyright policy )$A_{\infty}$-coderivations and the Gerstenhaber bracket on Hochschild cohomology
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.
- University of North Carolina at Chapel Hill United States
- The University of Texas System United States
- Texas A&M University Main Campus United States
- Texas A&M University United States
- Negron Cris United States
Differential graded algebras and applications (associative algebraic aspects), Mathematics - Rings and Algebras, Hochschild cohomology, \(A_{\infty}\)-coderivations, \(A_{\infty}\)-coalgebras, Rings and Algebras (math.RA), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), FOS: Mathematics, Gerstenhaber bracket, Representation Theory (math.RT), Mathematics - Representation Theory
Differential graded algebras and applications (associative algebraic aspects), Mathematics - Rings and Algebras, Hochschild cohomology, \(A_{\infty}\)-coderivations, \(A_{\infty}\)-coalgebras, Rings and Algebras (math.RA), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), FOS: Mathematics, Gerstenhaber bracket, Representation Theory (math.RT), Mathematics - Representation Theory
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