2024-06-16T18:38:49Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/661832024-02-12T20:00:34Zcom_10324_1129com_10324_931com_10324_894col_10324_1193
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Brox, Jose
author
Fernández López, Antonio
author
Gómez Lozano, Miguel
author
2017
Let L be a Lie algebra over a ﬁeld F of characteristic zero or p > 3 . An element c ∈ L is called Cliﬀord if adc^3 = 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 . 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 ∈ Skew(R, ∗) be such that c^3 = 0 , c^2 != 0 and c^2kc = ckc^2 for all k ∈ Skew(R, ∗) . Then c is a Cliﬀord element of the Lie algebra Skew(R, ∗) .
Journal of Lie Theory, 2017, vol. 27, no. 1, p. 283-296
https://uvadoc.uva.es/handle/10324/66183
283
1
296
Journal of Lie Theory
27
Matemáticas
Clifford elements in Lie algebras