Quasi-Hopf $\ast$-Algebras

Abstract

We introduce quasi-Hopf $\ast$-algebras i.e. quasi-Hopf algebras equipped with a conjugation (star) operation. The definition of quasi-Hopf $\ast$-algebras proposed ensures that the class of quasi-Hopf $\ast$-algebras is closed under twisting and additionally, that any Hopf $\ast$-algebra becomes a quasi-Hopf $\ast$-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 $\ast$-algebras are introduced and studied.

31 pages