On Nakayama automorphisms of double Frobenius algebras

Abstract

Double Frobenius algebras (or dF-algebras) were recently introduced by the author. The concept generalizes finite-dimensional Hopf algebras, adjacency algebras of (non-commutative) association schemes, and C-algebras (or character algebras). This paper studies basic properties of various Nakayama automorphisms in a dF-algebra. As an application the theorem of D. E. Radford, stating that the antipodeSof a finite-dimensional Hopf algebra is of finite order, is generalized to dF-algebras, and so is his formula for S4n in terms of certain group-like elements. © 1999 Academic Press.