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arXiv · 2503.13059

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

Ignacio Bajo·Saïd Benayadi·Hassan Oubba
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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. Bre\v{s}ar and K. Zhao.

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Ignacio Bajo, Saïd Benayadi, Hassan Oubba. 2025-03-17. Non-existence of symmetric biderivations on finite-dimensional perfect Lie algebras. https://arxiv.org/abs/2503.13059

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