|
|
Pure Mathematics 2025
相容的Rota-Baxter约当代数
|
Abstract:
本文探讨了Rota-Baxter约当代数的表示及二维约当代数上可容许的伴随线性映射的构造。首先，引入了Rota-Baxter约当代数的定义，然后研究了两个Rota-Baxter约当代数相容的条件。最后构造了二维Rota-Baxter约当代数上可容许的伴随线性映射。
This paper explores the representation of Jordan algebra and the construction of adjoint-admissiable linear map on two-dimensional Jordan algebra. First, the definition of Rota-Baxter Jordan algebra is introduced. Then, the equivalent condition of two compatible Rota-Baxter Jordan algebras is studied. Finally, adjoint-admissiable linear map on two-dimensional Jordan algebra is constructed.
| [1] | Albert, A.A. (1947) A Structure Theory for Jordan Algebras. The Annals of Mathematics, 48, 546-567. https://doi.org/10.2307/1969128 |
| [2] | Jacobson, N. (1949) Lie and Jordan Triple Systems. American Journal of Mathematics, 71, 149-170. https://doi.org/10.2307/2372102 |
| [3] | Hou, D., Ni, X. and Bai, C. (2013) Pre-Jordan Algebras. Mathematica Scandinavica, 112, 19-48. https://doi.org/10.7146/math.scand.a-15231 |
| [4] | Bai, C., Guo, L., Liu, G. and Ma, T. (2024) Rota-Baxter Lie Bialgebras, Classical Yang-Baxter Equations and Special L-Dendriform Bialgebras. Algebras and Representation Theory, 27, 1347-1372. https://doi.org/10.1007/s10468-024-10261-1 |
| [5] | Sun, Y., Huang, Z. and Zhao, S. (2021) Classification of Pre-Jordan Algebras and Rota-Baxter Operators on Jordan Algebras in Low Dimensions. arXiv: 2111.02035. |
| [6] | Golubchik, I.Z. and Sokolov, V.V. (2006) Compatible Lie Brackets and the Yang-Baxter Equation. Theoretical and Mathematical Physics, 146, 159-169. https://doi.org/10.1007/s11232-006-0016-6 |
| [7] | Wu, M. and Bai, C. (2015) Compatible Lie Bialgebras. Communications in Theoretical Physics, 63, 653-664. https://doi.org/10.1088/0253-6102/63/6/653 |
| [8] | Jacobson, N. (1951) General Representation Theory of Jordan Algebras. Transactions of the American Mathematical Society, 70, 509-530. https://doi.org/10.1090/s0002-9947-1951-0041118-9 |
| [9] | 贾超. 相容Jordan代数与BiHom-Jordan代数的表示[D]: [硕士学位论文]. 大连: 辽宁师范大学, 2021. |
