Rota‐Baxter Operators on 3‐Dimensional Lie Algebras and the Classical R‐Matrices

Linli Wu, Mengping Wang and Yongsheng Cheng

Advances in Mathematical Physics, 2017, vol. 2017, issue 1

Abstract: Our aim is to classify the Rota‐Baxter operators of weight 0 on the 3‐dimensional Lie algebra whose derived algebra’s dimension is 2. We explicitly determine all Rota‐Baxter operators (of weight zero) on the 3‐dimensional Lie algebras g. Furthermore, we give the corresponding solutions of the classical Yang‐Baxter equation in the 6‐dimensional Lie algebras g ⋉ad⁎ g⁎ and the induced left‐symmetry algebra structures on g.

Date: 2017
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https://doi.org/10.1155/2017/6128102

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:6128102

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