Non-existence of symmetric biderivations on finite-dimensional perfect Lie algebras

2025/03/17 by Bajo, Ignacio, Benayadi, Saïd, Oubba, Hassan · 1 citation
#17A20 #17A32 #17A60 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2503.13059

Abstract

We show that there are no symmetric non-zero biderivations on perfect Lie algebras of finite dimension over a field of characteristic zero. We show that this is equivalent to show that every symmetric biderivation on a finite-dimensional perfect Lie algebra over such a field with values in a finite-dimensional module vanishes identically. This answers an open question posed by M. Brešar and K. Zhao.

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