Nilpotent linear transformations and the solvability of power-associative nilalgebras

Date
2005-02-01
Authors
Correa, Ivan
Hentzel, Irvin
Julca, Pedro
Peresi, Luiz
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Mathematics
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Abstract

We prove some results about nilpotent linear transformations. As an application we solve some cases of Albert’s problem on the solvability of nilalgebras. More precisely, we prove the following results: commutative power-associative nilalgebras of dimension n and nilindex n − 1 or n − 2 are solvable; commutative power-associative nilalgebras of dimension 7 are solvable.

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This article is published as Correa, Ivan, Irvin Roy Hentzel, Pedro Pablo Julca, and Luiz Antonio Peresi. "Nilpotent linear transformations and the solvability of power-associative nilalgebras." Linear algebra and its applications 396 (2005): 35-53. doi:10.1016/j.laa.2004.08.007. Posted with permission.

Keywords
Nilpotent linear transformations, Commutative, Power-associative, Nilalgebra, Albert’s problem, Solvable, Nilpotent
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