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<p>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 Brešar and Zhao (J Lie Theory 28, 885–900, 2018).</p>

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Non-existence of Symmetric Biderivations on Finite-Dimensional Perfect Lie Algebras

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • Ignacio Bajo,
  • Saïd Benayadi,
  • Hassan Oubba

摘要

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 Brešar and Zhao (J Lie Theory 28, 885–900, 2018).