A classical theorem of Amitsur states that any proper prime T-ideal in a free algebra is the ideal of polynomial identities of the algebra of n × n matrices for some n. Moreover the associated relatively free algebra has a very interesting structure which has been extensively studied. We give a similar theorem in the context of trace identities classifying prime T-ideals of the trace algebra containing the n-Cayley-Hamilton identity and discuss the corresponding relatively free algebras from algebraic and geometric points of view. One has a one-to-one correspondence between these T-ideals and semisimple n-Cayley-Hamilton algebras and also the strata of the so-called Luna stratification for the quotient variety of k-tuples of n × n matrices under the conjugation action of the projective group.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
