Clifford elements in Lie algebras
Let L be a Lie algebra over a field
F of characteristic zero or p > 3. An element c in L is
called Clifford if adc3 = 0 and its associated Jordan algebra
Lc is the Jordan algebra F + X defined by a
symmetric bilinear form on a vector space X over F.
Roughly speaking, we prove in this note that c is a Clifford
element if and only if there exists a centrally closed prime ring
R with involution * such that c belongs to Sk(R,*), the skew elements of R with
respect to *, c3 = 0,
c2 ≠ 0 and c2 k c = c k c2 for all k in Sk(R,*).
(This paper has appeared in Journal of Lie Theory, vol. 27 (2017), 283-296)
J. Brox < brox@agt.cie.uma.es >
A. Fernández López < emalfer@uma.es >
M. Gómez Lozano < magomez@agt.cie.uma.es >