A note on inner actions of Hopf algebras

Caenepeel, Stefaan

doi:10.1090/S0002-9939-1991-1069684-6

A note on inner actions of Hopf algebras
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Proc. Amer. Math. Soc. 113 (1991), 31-39 Request permission

Abstract:

Let $H$ be a commutative, cocommutative, and faithfully projective Hopf algebra over a commutative ring $R$. A twisted version of inner action of a Hopf algebra, called $H$-inner action is introduced, and it is shown that $H$ acts $H$-innerly on an $H$-Azumaya algebra, if $\operatorname {Pic} ({H^ * })$ is trivial.

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