An online session of the Algebra and Logic Seminar will be held on April 29, 2022 (Friday) at 4:00 pm (UTC+3).
A talk on:
Images of multilinear polynomials on upper triangular matrices
will be delivered by Thiago Castilho de Mello (Universidade Federal de São Paulo, Brazil).
Abstract.
Let f(x1, …, xm) be a polynomial in noncommutative variables over an infinite field K. If A is a K-algebra, it defines in a natural way a map Am → A. If the polynomial f is multilinear, the famous Lvov-Kaplansky conjecture asks whether the image of a multilinear polynomial on a matrix algebra is a vector subspace. Solutions to this problem are known only for n = 2 or m = 2 with partial results for m = 3 and n = 3.
In this talk, we survey these results and discuss possible variations for this problem in the associative and nonassociative settings.
In particular, we discuss a joint work with I. Gargate about images of multilinear polynomials on upper triangular matrices.
The seminar will be held via Zoom and anyone can join at:
https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09
Topic: Онлайн семинар на секция “Алгебра и логика”
Time: Apr 29, 2022 04:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647
Algebra and Logic Department, IMI-BAS
http://www.math.bas.bg/algebra/seminarAiL/
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