Cohomology of the adjoint of Hopf algebras

Authors

J. Scott Carter, University of South Alabama
Alissa S. Crans, Loyola Marymount UniversityFollow
Mohamed Elhamdadi, University of South Florida
Masahico Saito, University of South Florida

Document Type

Article

Publication Date

2007

Abstract

A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of the super line. As applications, solutions to the YBE are given and quandle cocycles are constructed from groupoid cocycles.

Digital Commons @ LMU & LLS Citation

Carter, J.S.; Crans, A.; Elhamdadi, M.; and Saito, M. “Cohomology of the adjoint of Hopf algebras.” Journal of Generalized Lie Theory and Applications, Vol. 2 (2008), No. 1: 19 – 34.