The L'vov-Kaplansky conjecture and some of its variations

Abstract: The L'vov-Kaplansky conjecture claims that the image of a multilinear polynomial on the full matrix algebra is a vector space. Positive results concerning the conjecture are known only for small cases (polynomials of small degree or matrices of small size). Besides presenting the main results on the L'vov-Kaplasnky conjecture, in this talk we also will discuss some of its variations such as images of multilinear polynomials on some subalgebras of the full matrix algebra with additional structure (gradings, involutions, graded involutions).

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar