2023/12/23 by Niels Kowalzig, Kowalzig, Niels
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2312.15278
openalex publication_date 2023/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that if an operad is at the same time a cosimplicial object such that the respective structure maps are compatible with the operadic composition in a natural way, then one obtains a Gerstenhaber algebra structure on cohomology, and if the operad is cyclic, even that of a BV algebra. In particular, if a cyclic opposite module over an operad with multiplication is itself a cyclic operad that meets the cosimplicial compatibility conditions, the cohomology of its cyclic dual turns into a BV algebra. This amounts to conditions for when the cyclic dual of a BV module is endowed with a BV algebra structure, a result we exemplify by looking at classical and less classical (co)homology groups in Hopf algebra theory.