Louis Rowen

Louis Rowen

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Louis Rowen

Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel

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Academic Career Length

45Years (1982-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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16 June 2011 in Proceedings of the American Mathematical Society
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Alexey Yakovlevich Kanel-BelovAlexey Yakovlevich Kanel-Belov
Alexey Yakovlevich Kanel-Belov
SMSergey Malev
Sergey Malev
LRLouis Rowen
Louis Rowen
Let p p be a multilinear polynomial in several non-commuting variables with coefficients in a quadratically closed field K K of any characteristic. It has been conjectured that for any n n , the image of p p evaluated on the set M n ( K ) M_n(K) of n n by n n matrices is either zero, or the set of scalar matrices, or the set s l n ( K ) sl_n(K) of matrices of trace 0, or all of M n ( K ) M_n(K) . We prove the conjecture for n = 2 n=2 , and show that although the analogous assertion fails for completely homogeneous polynomials, one can salvage the conjecture in this case by including the set of all non-nilpotent matrices of trace zero and also permitting dense subsets of M n ( K ) M_n(K) .
1 March 2011 in Israel Journal of Mathematics
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ZIZur Izhakian
Zur Izhakian
LRLouis Rowen
Louis Rowen
1 November 2011 in Israel Journal of Mathematics
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ZIZur Izhakian
Zur Izhakian
LRLouis Rowen
Louis Rowen
11 September 2015 in Proceedings of the American Mathematical Society
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Alexey Yakovlevich Kanel-BelovAlexey Yakovlevich Kanel-Belov
Alexey Yakovlevich Kanel-Belov
SMSergey Malev
Sergey Malev
LRLouis Rowen
Louis Rowen
Let p p be a multilinear polynomial in several noncommuting variables, with coefficients in an algebraically closed field K K of arbitrary characteristic. In this paper we classify the possible images of p p evaluated on 3 × 3 3\times 3 matrices. The image is one of the following: {0}, the set of scalar matrices, a (Zariski-)dense subset of sl 3 ⁡ ( K ) \operatorname {sl}_3(K) , the matrices of trace 0, a dense subset of M 3 ( K ) M_3(K) , the set of 3 3 -scalar matrices (i.e., matrices having eigenvalues ( β , β ε , β ε 2 ) ( \beta , \beta \varepsilon , \beta \varepsilon ^2) where ε \varepsilon is a cube root of 1), or the set of scalars plus 3 3 -scalar matrices.
1 October 2014 in Journal of Algebra
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ZIZur Izhakian
Zur Izhakian
MKManfred Knebusch
Manfred Knebusch
LRLouis Rowen
Louis Rowen
12 October 2021 in European Journal of Mathematics
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LRLouis Halle Rowen
Louis Halle Rowen