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HEBREW UNIVERSITY

Amitsur Algebra Seminar
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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>

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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il>
Announcement from: Konstantin Golubev   <kgolubev@gmail.com>