Cup Coproducts in Hopf Cyclic Cohomology
Mohammad Hassanzadeh, Masoud Khalkhali
TL;DR
This paper introduces cup coproducts in Hopf cyclic cohomology, connecting them to classical coproducts in Lie algebra and group homology, thus enriching the algebraic structure of Hopf cyclic cohomology.
Contribution
It defines cup coproducts for Hopf cyclic cohomology and its dual, establishing their compatibility with known coproducts in classical homology theories.
Findings
Coproducts recover standard Lie algebra homology coproducts
Coproducts recover standard group homology coproducts
Provides new algebraic structures in Hopf cyclic cohomology
Abstract
We define cup coproducts for Hopf cyclic cohomology of Hopf algebras and for its dual theory. We show that for universal enveloping algebras and group algebras our coproduct recovers the standard coproducts on Lie algebra homology and group homology, respectively.
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