Gradings by Groups on Classical Simple Algebras
by
Yuri Bahturin
Memorial University of Newfoundland and Moscow State University

If A is an algebra over a field F and G a group then a very general fact is that

the gradings of A by G are equivalent to the natural actions of a Hopf algebra

H=(FG)* dual to the group algebra FG. The structure of the coproduct in H is not

simple but in certain cases H is just the group algebra of the group of characters

of G, in some others H is a restricted enveloping algebra of a Lie algebra of

derivations of FG with values in F, etc. In our talk we would like to discuss the

methods arising and the results on the gradings of simple algebras of various

classes which have been obtained using these methods.

Date received: March 30, 2006