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arXiv · 2211.06645

A $\delta$-first Whitehead Lemma

Arezoo Zohrabi·Pasha Zusmanovich
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Abstract

We prove that $\delta$-derivations of a simple finite-dimensional Lie algebra over a field of characteristic zero, with values in a finite-dimensional module, are either inner derivations, or, in the case of adjoint module, multiplications by a scalar, or some exceptional cases related to $\mathfrak{sl}(2)$. This can be viewed as an extension of the classical first Whitehead Lemma.

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Arezoo Zohrabi, Pasha Zusmanovich. 2022-11-12. A $\delta$-first Whitehead Lemma. https://doi.org/10.1016/j.jalgebra.2020.12.040

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