Biderivations and commutative post-Lie algebra structure on the Schr\"odinger-Virasoro Lie algebra

TL;DR

This paper characterizes biderivations of the Schr"odinger-Virasoro Lie algebra and explores the resulting commutative post-Lie algebra structures, revealing new types of derivations beyond the inner and skew-symmetric cases.

Contribution

It provides a complete characterization of biderivations and introduces new commutative post-Lie algebra structures on the Schr"odinger-Virasoro Lie algebra.

Findings

Identified classes of non-inner, non-skewsymmetric biderivations.

Characterized commutative post-Lie algebra structures on the algebra.

Extended understanding of derivations in infinite-dimensional Lie algebras.

Abstract

In this paper, we characterize the biderivations of Schr\"odinger-Virasoro Lie algebra. We get a classes of non-inner and non-skewsymmetric biderivations. As application, we characterize the commutative post-Lie algebra structures on Schr\"odinger-Virasoro Lie algebra.