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Mathematics > Rings and Algebras

Title: A $δ$-first Whitehead Lemma for Jordan algebras

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.
Comments: 8 pages
Subjects: Rings and Algebras (math.RA)
MSC classes: 17C20, 17C55, 17A36
Cite as: arXiv:2404.11966 [math.RA]
  (or arXiv:2404.11966v1 [math.RA] for this version)

Submission history

From: Pasha Zusmanovich [view email]
[v1] Thu, 18 Apr 2024 07:53:20 GMT (11kb)

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