On finite order elements in Hopf algebras over rings

Research Report MRR98-056

On finite order elements in Hopf algebras over rings

Lars Kadison and A.A. Stolin

Abstract: It was recently shown in [9] that for any Hopf algebra H over a field k the antipod S and the Nakayama automorphism $\eta$ have order dividing 4 dim H and 2 dim H respectively. The purpose in this paper is to generalize these results for finite projective Hopf algebras over Noetherian rings. To do this we need a sharp estimate on the order of a group-like element of H. Using a formula for

and a formula relating the Nakayama automorphism $\eta$ with

, we obtain estimates for orders of S and $\eta$ , which coincide in the case of fields with that of [9].

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Download paper:	PDF file (188K)
	gzipped DVI file (17K)

Download cover sheet:	PDF file (51K)
	DVI file (2K)