Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 27 (2017), No. 1, 283--296Copyright Heldermann Verlag 2017 Clifford Elements in Lie Algebras José Ramón Brox Dep. de Álgebra, Geometría y Topología, Universidad de Málaga, 29071 Málaga, Spain brox@agt.cie.uma.es Antonio Fernández López Dep. de Álgebra, Geometría y Topología, Universidad de Málaga, 29071 Málaga, Spain emalfer@uma.es Miguel Gómez Lozano Dep. de Álgebra, Geometría y Topología, Universidad de Málaga, 29071 Málaga, Spain miggl@uma.es [Abstract-pdf] \def\F{\mathbb{F}} \def\sk{{\rm Skew}} \def\ad{\mathop{\rm ad}\nolimits} Let $L$ be a Lie algebra over a field $\F$ of characteristic zero or $p>3$. An element $c\in L$ is called {\it Clifford} if $\ad_c^3=0$ and its associated Jordan algebra $L_c$ is the Jordan algebra $\F \oplus X$ defined by a symmetric bilinear form on a vector space $X$ over $\F$. 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 $\sk(R,*)$. Keywords: Lie algebra, ring with involution, Jordan algebra, inner ideal, Jordan element. MSC: 17B60, 17C50, 16N60 [ Fulltext-pdf  (285  KB)] for subscribers only.