| On Modified Rota-Baxter Hom-Lie Algebras |
| Received:January 25, 2024 Revised:May 23, 2024 |
| Key Words:
Hom-Lie algebra modified Rota-Baxter operator cohomology deformation abelian extension
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| Fund Project:Supported by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province (Grant No.2023013), the National Natural Science Foundation of China (Grant No.12161013) and the Science and Technology Program of Guizhou Province (Grant No.ZK[2023]025). |
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| Abstract: |
| Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified $r$-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified Rota-Baxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2025.02.003 |
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