Arezoo Zohrabi ; Pasha Zusmanovich - A $\delta$-first Whitehead Lemma for Jordan algebras

cm:13595 - Communications in Mathematics, October 11, 2024, Volume 33 (2025), Issue 1 - https://doi.org/10.46298/cm.13595
A $\delta$-first Whitehead Lemma for Jordan algebrasArticle

Authors: Arezoo Zohrabi ; Pasha Zusmanovich

    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.


    Volume: Volume 33 (2025), Issue 1
    Published on: October 11, 2024
    Accepted on: July 16, 2024
    Submitted on: May 16, 2024
    Keywords: Mathematics - Rings and Algebras,17C20, 17C55, 17D99

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