=-=-=-=-=-=-=-=-=-=-= HEBREW UNIVERSITY Amitsur Algebra Seminar ---------------------------------- Time: Thursday, May 30, 12:00-13:15 Place: math 209 Title: Images of multilinear polynomials evaluated on the matrices of arbitrary order. Speaker: Sergey Malev (Bar-Ilan) Abstract: There is a Kaplansky problem: the only possible images of multilinear polynomial evaluated on $n\times n$ matrices $M_n(K)$ are $\{0\},$ $K,$ $sl_n(K)$ or $M_n(K)$, where $K$ is the set of scalar matrices. We established Kaplansky problem for $n=2$. For the case $n=3$ the situation is as follows: the only possible images are $\{0\},$ $K,$ Image p is dense in $sl_3(K)$ or dense in $M_3(K)$. In particular I would like to show that almost all non diagonalisible matrices lay in Image $p$ (if Im $p$ is dense in $M_3(K).$ For the general case of arbitrary $n$ I would like to say about our general result: the only possible images of multilinear polynomial evaluated on $n\times n$ matrices $M_n(K)$ are $\{0\},$ $K$, the dense subset of $sl_n(K)$ or the dense subset of $M_n(K)$. You are cordially invited! <http://ma.huji.ac.il/amitsur.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Konstantin Golubev <kgolubev@gmail.com>