Indecomposable Hopf $\ast$-algebra representations with invariant inner product

Abstract

We generalize a result of Araki (1985) on indecomposable group representations with invariant (necessarily indefinite) inner product and irreducible subrepresentation to Hopf $\ast$-algebras. Moreover, we characterize invariant inner products on the projective indecomposable representations of small quantum groups $U_{q}sl(2)$ at odd roots of unity and on the indecomposable representations of generalized Taft algebras $H_{n,d}(q)$.

10 pages. Minor edits to correct typos