The lazy homology of a Hopf algebra

Details The lazy homology of a Hopf algebra The lazy homology of a Hopf algebra

2008-07-10

arxiv.org/abs/0807.1651v1

Journal of Algebra 323 (2010), 2556-2590

Mathematics

Quantum Algebra

28 pages

Scientific paper

10.1016/j.jalgebra.2009.12.032

To any Hopf algebra H we associate two commutative Hopf algebras, which we call the first and second lazy homology Hopf algebras of H. These algebras are related to the lazy cohomology groups based on the so-called lazy cocycles of H by universal coefficient theorems. When H is a group algebra, then its lazy homology can be expressed in terms of the 1- and 2-homology of the group. When H is a cosemisimple Hopf algebra over an algebraically closed field of characteristic zero, then its first lazy homology is the Hopf algebra of the universal abelian grading group of the category of corepresentations of H. We also compute the lazy homology of the Sweedler algebra.

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