A delta-first Whitehead Lemma

摘要

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 sl(2). This can be viewed as an extension of the classical first Whitehead Lemma. (C) 2021 Elsevier Inc. All rights reserved.