An approach to Hopf algebras via Frobenius coordinates II

Details An approach to Hopf algebras via Frobenius coordinates II An approach to Hopf algebras via Frobenius coordinates II

2001-03-05

arxiv.org/abs/math/0103019v1

Mathematics

Rings and Algebras

22 pages

Scientific paper

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.

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