(43). Clifford elements in Lie algebras.

Autores: Jose Brox, Antonio Fernández López and Miguel Gómez Lozano.  

Revista: Journal of Lie Theory 27, (2017) 283-296. (230 de 310 Factor de impacto: 0.529 en 2017)

Abstract:Let $L$ be a Lie algebra over a field $\mathbb F$ of characteristic zero or $p > 3$. An element $c \in L$ is called Clifford if $\ad_c^3=0$ and its associated Jordan algebra $L_c$ is the Jordan algebra $\mathbb F \oplus X$ defined by a symmetric bilinear form on a vector space $X$ over $\mathbb F$. In this paper we prove the following result: Let $R$ be a centrally closed prime ring $R$ of characteristic zero or $p > 3$ with involution $*$ and let $c \in \sk(R,*)$ be such that $c^3=0$, $c^2 \neq 0$ and $c^2kc =ckc^2$ for all $k \in \sk(R,*)$. Then $c$ is a Clifford element of the Lie algebra $\sk(R,*)$.