Rota-Baxter operators on filiform Lie algebras <inline-formula> <mml:math> <mml:mrow> <mml:msub> <mml:mi mathvariant="fraktur">L</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> </inline-formula> and <inline-formula> <mml:math> <mml:mrow> <mml:msub> <mml:mi mathvariant="fraktur">L</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> </inline-formula> L 3 and L 4 " /> L 3 and L 4 " />

Research Article

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

Published in: Quaestiones Mathematicae
Volume 48 , issue 8 , 2025 , 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
Download full text Get new issue alerts

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 .
« A note on the construction of non-spatial frames
On β-adic expansions of powers of an algebraic integer omitting a digit »

Get new issue alerts for Quaestiones Mathematicae

Latest news

   more...

Latest articles

   more...