The images of non-commutative polynomials evaluated on $2\times 2$ matrices

Details The images of non-commutative polynomials evaluated on $2\times 2$ matrices The images of non-commutative polynomials evaluated on $2\times 2$ matrices

2010-05-03

arxiv.org/abs/1005.0191v3

Mathematics

Algebraic Geometry

Scientific paper

Let $p$ be a multilinear polynomial in several non-commuting variables with coefficients in a quadratically closed field $K$ of any characteristic. It has been conjectured that for any $n$, the image of $p$ evaluated on the set $M_n(K)$ of $n$ by $n$ matrices is either zero, or the set of scalar matrices, or the set $sl_n(K)$ of matrices of trace 0, or all of $M_n(K)$. We prove the conjecture for $n=2$.

Affiliated with

Also associated with

No associations

Rating

The images of non-commutative polynomials evaluated on $2\times 2$ matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The images of non-commutative polynomials evaluated on $2\times 2$ matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The images of non-commutative polynomials evaluated on $2\times 2$ matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-658098