Conference abstracts

Session S05 - Rings and Algebras

July 29, 15:45 ~ 16:10

Graded algebras and polynomial identities

Eli Aljadeff

Technion, Haifa, Israel   -

Connections (or ``bridges'') between PI theory (polynomial identities) and group gradings on associative algebras are quite well known for more than 30 years. For instance, Kemer applied the theory of ``super algebras'' in order to solve the famous Specht problem for nonaffine PI algebras. Our interest is in the opposite direction. We apply PI theory in order to solve a conjecture of Bahturin and Regev on ``regular G-gradings'' on associative algebras where G is a finite abelian group. Moreover, we show how to extend it to nonabelian groups. As a second application, we present a Jordan's like theorem on G-gradings on associative algebras.

Joint work with Ofir David (Technion, Israel).

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