Tracing cyclic homology pairings under twisting of graded algebras

2017/09/11 by Chakraborty, Sayan, Yamashita, Makoto
#FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1709.03337

Abstract

We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss-Manin connection on periodic cyclic cohomology in terms of the cup product action of group cohomology.

Related

• Monodromy of the Gauss-Manin connection for deformation by group cocycles
• The Gauss-Manin connection on the periodic cyclic homology
• Exponentially twisted cyclic homology
• Cyclic cohomology for graded C^*,r-algebras and its pairings with van Daele K-theory
• Cyclic Cohomology of Hopf algebras and Hopf Algebroids