Cycles over DGH-semicategories and pairings in categorical Hopf-cyclic\n cohomology

2019/01/28 by Mamta Balodi, Abhishek Banerjee, Balodi, Mamta +1
Mathematics · #16T05 #18E05 #58B34 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1901.09580

openalex publication_date 2019/01/28 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

Let H be a Hopf algebra and let mathcal D_H be a Hopf-module category.\nWe describe the cocycles and coboundaries for the Hopf cyclic cohomology of\n mathcal D_H, which correspond respectively to categorified cycles and\nvanishing cycles over mathcal D_H. An important role in our work is played\nby semicategories, which are categories that may not contain identity maps. In\nparticular, a cycle over mathcal D_H consists of a differential graded\nH-module semicategory equipped with a trace on endomorphism groups satisfying\nsome conditions. Using a pairing on cycles, we obtain a pairing\nHC^p(\C) \⊗ HC^q(\C') longrightarrow\nHC^p+q(\C \⊗ \C') on cyclic cohomology groups for\nsmall k-linear categories mathcal C and mathcal C'.\n

Citations

• Morita invariance of equivariant and Hopf-cyclic cohomology of module algebras over Hopf algebroids

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