Representation Theory of Noetherian Hopf Algebras Satisfying a Polynomial Identity
نویسنده
چکیده
A class of Noetherian Hopf algebras satisfying a polynomial identity is axiomatised and studied. This class includes group algebras of abelian-by-nite groups, nite dimensional restricted Lie algebras, and quantised enveloping algebras and quantised function algebras at roots of unity. Some common homological and representation-theoretic features of these algebras are described, with some indications of recent and current developments in research on each of the exemplar classes. It is shown that the nite dimensional representation theory of each of these algebras H reduces to the study of a collection Alg(H) of ((nite dimensional) Frobenius algebras. The properties of this family of nite dimensional algebras are shown to be intimately connected with geometrical features of central sub-Hopf algebras of H. A number of open questions are listed throughout.
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