Indecomposable Hopf *-algebra representations with invariant inner product

2024/11/03 by Quinn T. Kolt, Kolt, Quinn T., Zhao, Ziqian
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2411.01463

Abstract

We generalize a result of Araki (1985) on indecomposable group representations with invariant (necessarily indefinite) inner product and irreducible subrepresentation to Hopf *-algebras. Moreover, we characterize invariant inner products on the projective indecomposable representations of small quantum groups U_qsl(2) at odd roots of unity and on the indecomposable representations of generalized Taft algebras H_n,d(q).

Related

• Representation theory of a Class of Hopf algebras
• Hopf algebras with trace and representations
• Residually finite quantum group algebras
• Indecomposable decomposition of tensor products of modules over Drinfeld Doubles of Taft algebras
• Representations of cross product algebras of Podles quantum spheres