Research Article

Rota-Baxter operators on filiform Lie algebras L 3 and L 4

Published in: Quaestiones Mathematicae
Volume 48 , issue 8 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 1225–1246
DOI: 10.2989/16073606.2025.2475235
Author(s): Jinwei Su Tongji University, China, Xiaoqing Yue Tongji University, China,
Keywords: 17B38, 17B30, 16T25, Rota-Baxter operators, filiform Lie algebras, Yang-Baxter equation, left-symmetric algebras,
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Abstract

In this paper, we completely determine all the Rota-Baxter operators on the 3-dimensional filiform Lie algebra and the 4-dimensional filiform Lie algebra . As an application of Rota-Baxter operators, we derive the skew-symmetric solutions of the classical Yang-Baxter equation in the Lie algebras and , and construct the corresponding left-symmetric algebra structures on and .
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