Graded algebras and polynomial identities

Speaker: Eli Aljadeff, Technion, Israel Institute of Technology.

Connections (or "bridges'') between PI theory (polynomial identities) and group gradings on associative algebras are quite well known for more than 30 years,
where applications appear in both directions.

For instance, Kemer applied the theory of "super algebras'' in order to solve the famous Specht problem (to be explained in the lecture) for nonaffine PI algebras. In the other direction, PI theory is used in order to solve a conjecture of Bahturin and Regev on "regular gradings'' on associative algebras over a field of characteristic zero.

The purpose of this lecture is to present a (Jordan's like) theorem on G-gradings on associative algebras which is obtained from such a bridge.

In the lecture I'll explain the basic notions involved.