Mathematical Sciences: Actions of Groups and Hopf Algebras

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This research concerns automorphism groups of rings and more generally, the actions of Hopf algebras. The principal investigator will examine those automorphisms of a ring which become inner on the two-sided quotient ring of the ring, as well as the generalized Picard group. Non-abelian extensions of Hopf algebras will also be considered. This research is in the general area of noncommutative ring theory. It concerns the actions of Hopf algebras. This line of study is motivated in part by the study of group rings and representations of an affine algebraic group. In both of these cases the underlying coalgebra is commutative. This research will endeavor to remove the commutativity restriction.