Cyclic brace relation and BV structure on open-closed Hochschild cohomology

2025/11/06 by Hang Yuan, Yuan, Hang
Mathematics · #Advanced Combinatorial Mathematics #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.2511.04095

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

For an open-closed homotopy algebra (OCHA), the previous work indicates that there is an open-closed version of Hochschild cohomology with a canonical Gerstenhaber algebra structure. If this OCHA is further cyclic and unital in the sense of Kajiura and Stasheff, we produce a BV algebra structure on this cohomology via a cochain-level identity formulated with cyclic brace operations.

Citations

• Open-Closed Hochschild Homology and the Relative Disk Mapping Space
• An open-closed string analogue of Hochschild cohomology
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• The Hochschild cohomology ring of a Frobenius algebra with semisimple\n Nakayama automorphism is a Batalin-Vilkovisky algebra
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• Calabi-Yau algebras
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