A note on inner actions of Hopf algebras

Abstract

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