A $δ$-first Whitehead Lemma for Jordan algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916439499210752 |
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| author | Zohrabi, Arezoo Zusmanovich, Pasha |
| author_facet | Zohrabi, Arezoo Zusmanovich, Pasha |
| contents | We compute $δ$-derivations of simple Jordan algebras with values in irreducible bimodules. They turn out to be either ordinary derivations ($δ= 1$), or scalar multiples of the identity map ($δ= \frac 12$). 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11966 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A $δ$-first Whitehead Lemma for Jordan algebras Zohrabi, Arezoo Zusmanovich, Pasha Rings and Algebras 17C20, 17C55, 17D99 We compute $δ$-derivations of simple Jordan algebras with values in irreducible bimodules. They turn out to be either ordinary derivations ($δ= 1$), or scalar multiples of the identity map ($δ= \frac 12$). 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. |
| title | A $δ$-first Whitehead Lemma for Jordan algebras |
| topic | Rings and Algebras 17C20, 17C55, 17D99 |
| url | https://arxiv.org/abs/2404.11966 |