Non-existence of symmetric biderivations on finite-dimensional perfect Lie algebras
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. Bresar and K. Zhao.
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