# Evaluation of non-commutative polynomials on a quaternion algebra

Seminar

Speaker

Dr. Sergey Malev (Ariel University)

Date

13/11/2019 - 11:30 - 10:30Add to Calendar

`2019-11-13 10:30:00``2019-11-13 11:30:00``Evaluation of non-commutative polynomials on a quaternion algebra``Let p be a multilinear polynomial in several non-commuting variables, with coefficients in an arbitrary field K. Kaplansky conjectured that for any n, the image of p evaluated on the set M_n(K) of nxn matrices is a vector space. We settle the analogous conjecture for a quaternion algebra.``Third floor seminar room (room 201, building 216)``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room (room 201, building 216)

Abstract

Let p be a multilinear polynomial in several non-commuting variables, with coefficients in an arbitrary field K. Kaplansky conjectured that for any n, the image of p evaluated on the set M_n(K) of nxn matrices is a vector space. We settle the analogous conjecture for a quaternion algebra.

Last Updated Date : 02/11/2019