An approach to Hopf algebras via Frobenius coordinates II
Abstract
Description
We study a Hopf algebra $H$, which is finitely generated and projective over a commutative ring $k$, as a $P$-Frobenius algebra. We define modular functions in this setting, and provide a complete proof of Radford's formula for the fourth power of the antipode, using Frobenius algebraic techniques. As further applications, we extend Etingof and Gelaki's result that a separable and coseparable Hopf algebra has antipode of order two, the result of Schneider that Hopf subalgebras are twisted Frobenius extensions, and show that the quantum double is always a Frobenius algebra.
22 pages
22 pages