Biderivations of Simple Modular Lie Algebras of Cartan-Type

Wei Bai () and Wende Liu
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Wei Bai: School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China
Wende Liu: School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China

Mathematics, 2025, vol. 13, issue 16, 1-14

Abstract: Assume that L is a simple Lie algebra of Cartan-type over an algebraically closed field with a characteristic p > 3 . We demonstrate that all symmetric biderivations vanish by using weight space decompositions relative to a suitable torus and the standard Z -grading structures of L . We then conclude that every biderivation of L is inner, based on a general result concerning skew-symmetric biderivations. As the direct applications, we determine the linear commuting maps and commutative post-Lie algebra structures on L completely.

Keywords: Lie algebras of cartan-type; biderivations; commuting maps; commutative post-Lie algebra structures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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