Gerstenhaber bracket on double Hochschild complex and deformation theory

1999/10/07 by Boris Shoikhet, Shoikhet, Boris
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9910043

4 pages, 1 figure

arxiv created 1999/10/07 · openalex publication_date 1999/10/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a differential and a Lie bracket on the space\linebreak \\Hom (A^{⊗ k}, A^{⊗ l})\,_{k,l≥ 0} for any associative algebra A. The restriction of this bracket to the space \\Hom (A^{⊗ k}, A)\,_{k≥ 0} is exactly the Gerstenhaber bracket. We discuss some formality conjecture related with this construction. We also discuss some applications to deformation theory.

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