Quasi-Hopf $*$-Algebras

Details Quasi-Hopf $*$-Algebras Quasi-Hopf $*$-Algebras

2006-04-25

arxiv.org/abs/math/0604520v1

Mathematics

Quantum Algebra

31 pages

Scientific paper

We introduce quasi-Hopf $*$-algebras i.e. quasi-Hopf algebras equipped with a conjugation (star) operation. The definition of quasi-Hopf $*$-algebras proposed ensures that the class of quasi-Hopf $*$-algebras is closed under twisting and additionally, that any Hopf $*$-algebra becomes a quasi-Hopf $*$-algebra via twisting. The basic properties of these algebras are developed. The relationship between the antipode and star structure is investigated. Quasi-triangular quasi-Hopf $*$-algebras are introduced and studied.

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