Jordan Dale Hill
IME-USP
*-Identities for Matrices.
Abstract: A polynomial identity (PI) for an algebra A is a polynomial f in non-commuting variables (an element of the free associative algebra) that vanishes for all substitutions from A.
If the algebra A is equipped with an involution *, one can consider *-PIs for A: polynomial identities in which the variables may appear with a *.
Our talk will be concerned with *-identities for the full matrix algebra M_n(F) together with * = t, the usual transpose involution, or * = s the symplectic involution.
We will begin with a discussion of the Amitsur-Levitzki Theorem and end by presenting some new results related to the Amitsur-Levitzki theorem, but in the setting of *-identities.