Primitive Lie PI-algebras

Cabrera, Miguel; López, Antonio

doi:10.1090/proc/15744

Primitive Lie PI-algebras
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by Miguel Cabrera and Antonio Fernández López

Proc. Amer. Math. Soc. 150 (2022), 2277-2285

DOI: https://doi.org/10.1090/proc/15744

Published electronically: March 4, 2022

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Abstract:

A Lie algebra $L$ is called primitive if it is prime, nondegenerate, and contains a nonzero Jordan element $a$ such that the attached Jordan algebra $L_a$ is primitive. In this paper we prove that every primitive Lie PI-algebra over a field of zero characteristic is simple and finite-dimensional over its centroid.

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