Mathematical Sciences: Actions of Groups and Hopf Algebras

本研究涉及环的自同构群等 一般来说，Hopf代数的作用。 校长 研究者将研究那些环的自同构， 在环的双侧商环上也成为内环， 广义Picard群 Hopf的非交换扩张 代数也将被考虑。 本文的研究是在非交换环的一般范畴内进行的 理论 它涉及的行动的霍普夫代数。 这行 研究的部分动机是研究群环， 仿射代数群的表示。 在这两 的情况下，底层余代数是交换的。 本研究 将奋进消除交换性限制。

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.