An Approach to Hopf Algebras via Frobenius Coordinates I
Lars Kadison, A. A. Stolin
Abstract
In Section 1 we introduce Frobenius coordinates in the general setting that includes Hopf subalgebras. In Sections 2 and 3 we review briefly the theories of Frobenius algebras and augmented Frobenius algebras with some new material in Section 3. In Section 4 we study the Frobenius structure of an FH-algebra H Par72 and extend two recent theorems in EG. We obtain two Radford formulas for the antipode in H and generalize in Section 7 the results on its order in FMS. We study the Frobenius structure on an FH-subalgebra pair in Sections 5 and 6. In Section 8 we show that the quantum double of H is symmetric and unimodular.
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