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pro vyhledávání: '"van Wyk, Leon"'
A subalgebra of the full matrix algebra Mn(K), K a field, satisfying the identity [x1, y1][x2, y2]...[xq, yq] = 0 is called a Dq subalgebra of Mn(K). In the paper we deal with the structure, conjugation and isomorphism problems of maximal Dq subalgeb
Externí odkaz:
http://arxiv.org/abs/2403.19557
Publikováno v:
In Journal of Algebra 1 November 2024 657:159-206
Publikováno v:
In Linear Algebra and Its Applications 1 October 2024 698:73-93
Let K be a field, then we exhibit two matrices in the full nxn matrix algebra M_{n}(K) which generate M_{n}(K) as a Lie K-algebra with the commutator Lie product. We also study Lie centralizers of a not necessarily commutative unitary algebra and obt
Externí odkaz:
http://arxiv.org/abs/2110.02534
Akademický článek
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For an nxn matrix A over a Lie nilpotent ring R of index k, we prove that an invariant "power" Cayley-Hamilton identity of degree (n^2)2^{k-2} holds. The right coefficients are not uniquely determined by A, and the cosets lambda_i+D, with D the doubl
Externí odkaz:
http://arxiv.org/abs/1909.10210
Autor:
Szigeti, Jeno, van Wyk, Leon
Publikováno v:
American Mathematical Monthly 124: pp. 966-968. (2017)
We give a constructive elementary proof for the fact that any K-automorphism of the full nxn matrix algebra over a field K is conjugation by some invertible nxn matrix A over K.
Externí odkaz:
http://arxiv.org/abs/1810.08368
Autor:
Szigeti, Jeno, van Wyk, Leon
We study certain (two-sided) nil ideals and nilpotent ideals in a Lie nilpotent ring R. Our results lead us to showing that the prime radical rad(R) of R comprises the nilpotent elements of R, and that if L is a left ideal of R, then L+rad(R) is a tw
Externí odkaz:
http://arxiv.org/abs/1501.00787
Publikováno v:
In Journal of Algebra 15 December 2020 564:247-275
Publikováno v:
In Linear Algebra and Its Applications 1 January 2020 584:153-163