An open-closed string analogue of Hochschild cohomology

2024/10/28 by Hang Yuan, Yuan, Hang · 2 citations
Mathematics · #16E40 #81T30 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2410.20888

openalex publication_date 2024/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every open-closed homotopy algebra, introduced by Kajiura and Stasheff (arXiv: archive/0410291), naturally gives rise to an open-closed version of Hochschild cochain complex whose cohomology admits a canonical Gerstenhaber algebra structure. We also develop the open-closed brace relations, provide a concise description of OCHAs, and establish an A-infinity structure that extends the open-closed Hochschild differential.

Cited by

• Open-Closed Hochschild Homology and the Relative Disk Mapping Space
• Cyclic brace relation and BV structure on open-closed Hochschild cohomology

Related

• Cyclic brace relation and BV structure on open-closed Hochschild cohomology
• Open-closed field theories, string topology, and Hochschild homology
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• Non-commutative calculus and Getzler-Gauss-Manin connections for Open-closed Homotopy Algebras
• Gerstenhaber algebra and Deligne's conjecture on Tate-Hochschild cohomology