Rota-Baxter operators on 3-dimensional Lie algebras and the classical \(R\)-matrices
type: Item
instance of: scholarly article
title: Rota-Baxter operators on 3-dimensional Lie algebras and the classical \(R\)-matrices
zbMATH Open document ID: 1437.17010
DOI: 10.1155/2017/6128102
author: Linli Wu
author: Mengping Wang
author: Yongsheng Cheng
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: Summary: 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 \(g \ltimes_{\mathrm{ad}^\ast} g^\ast\) and the induced left-symmetry algebra structures on \(g\).
Mathematics Subject Classification ID: 17B38
Mathematics Subject Classification ID: 16W25
zbMATH DE Number: 6962647
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/6128102
OpenAlex ID: W2779390601
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description: scientific article; zbMATH DE number 6962647