References & Citations
Mathematics > Rings and Algebras
Title: A $δ$-first Whitehead Lemma for Jordan algebras
(Submitted on 18 Apr 2024 (v1), last revised 14 May 2024 (this version, v2))
Abstract: We compute $\delta$-derivations of simple Jordan algebras with values in irreducible bimodules. They turn out to be either ordinary derivations ($\delta = 1$), or scalar multiples of the identity map ($\delta = \frac 12$). This can be considered as a generalization of the "First Whitehead Lemma" for Jordan algebras which claims that all such ordinary derivations are inner. The proof amounts to simple calculations in matrix algebras, or, in the case of Jordan algebras of a symmetric bilinear form, to more elaborated calculations in Clifford algebras.
Submission history
From: Pasha Zusmanovich [view email][v1] Thu, 18 Apr 2024 07:53:20 GMT (11kb)
[v2] Tue, 14 May 2024 06:18:05 GMT (11kb)
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