2014/09/16 by Jerry Lodder, Lodder, Jerry
Mathematics · #16E40 #81T40 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AT #math.QA #msc:16E40 #msc:81T40
paper · pdf · doi:10.48550/arxiv.1409.4825
19 pages
openalex publication_date 2014/09/16 · arxiv created 2015/06/16 · arxiv updated 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a Frobenius algebra structure on the Hochschild cochains of a group ring k[G] that extends the known structure of a <1, 2> topological quantum field theory on HH0(k[G]; k[G]), k a field and G a finite group. The convolution product extends to the homotopy commutative Gerstenhaber product on cochains, the Frobenius coproduct extends to a coproduct on the chain complex for Hochschild homology, and there is a pairing on Hochschild cocahins satisfying Frobenius associativity. The pairing, however, degenerates on a certain subcomplex of Hochschild cochains. The cochain complex for group cohomology under the simplicial cup product occurs as a homotopy commutative subalgebra of the Hochschild cochain complex under the Gerstenhaber product.