标题： 有限维完美李代数的对称双导子不存在 显示英文标题

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

摘要： 我们证明了在特征为零的域上有限维完美李代数上不存在非零对称双导子。 我们进一步证明，这等价于证明在这样的域上，有限维完美李代数取值于有限维模上的每个对称双导子恒等于零。 这回答了M. Brešar和K. Zhao提出的一个公开问题。 显示英文摘要

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 M. Bre\v{s}ar and K. Zhao.