Automatic additivity of multiplicative and Jordan multiplicative maps

Abstract: In this talk, we discuss the problem of automatic additivity for multiplicative maps between rings, following the classical results of Martindale and Jodeit-Lam. We present a complete description of Jordan multiplicative self-maps on full matrix algebras M_n(F), where F is a field of characteristic not equal to 2. Without imposing additional assumptions, we show that such maps are either constant (and equal to a fixed idempotent), or additive (and hence Jordan monomorphisms). This result is joint work with Ilja Gogić.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar