Claudio Procesi: The Amitsur—Levitzki theorem revisited and matrix identities

This seminar is in a way a “prequel” to Papi’s seminar on the exterior algebra of simple Lie algebras. I will give some classical background discussing 4 different types of matrix identities: namely polynomial identities, generalized polynomial identities, trace identities and quasi—identities and discuss various results and problems involved in these topics with a special look at the Amitsur—Levitzki theorem and the Cayley—Hamilton identity.