August 17, 2025Open Access

Biderivations of Simple Modular Lie Algebras of Cartan-Type

Key Points

All symmetric biderivations in simple lie algebras vanish, confirming their inner nature.
Using weight space decompositions and grading structures, a complete characterization of biderivations is achieved.
The findings allow for a comprehensive understanding of commuting maps within the algebra.
Implications extend to the formulation of commutative post-lie algebra structures on these algebras.

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.

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Cite This Study

Bai et al. (Wed,) studied this question.

synapsesocial.com/papers/68a36a360a429f797332e686 https://doi.org/https://doi.org/10.3390/math13162596

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