Conformal classical Yang–Baxter equation, S -equation and O -operators
Conformal classical Yang–Baxter equation, S -equation and O -operators
复制标题
DOI：
--
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Yanyong Hong;C. Bai;Y. Hong;C. Bai
中科院分区：
文献类型：
--
作者：
Yanyong Hong;C. Bai;Y. Hong;C. Bai
在李共形双代数和左对称共形双代数的研究中，自然地出现了共形经典Yang-Baxter方程和S方程。在本文中，它们被解释为一类算子，即共形意义上的O算子。明确地说，共形线性映射 T 的斜对称部分，其中 T 0 = T λ | λ = 0 是共形意义上的 O 算子，是共形经典 Yang-Baxter 方程的斜对称解，而对称部分是共形 S 方程的对称解。一个副产品是，作为自由 C [ ∂ ] 模的有限左对称共形代数给出了自然的 O 算子，因此，从前者可以构造出共形经典 Yang-Baxter 方程和共形 S 方程的解。另一个副产品是这两个方程的非简并解分别对应于李共形代数和左对称共形代数的 2-余循环。我们还进一步研究了李共形代数上一类特殊的 O 算子，称为 Rota–Baxter 算子，并给出了一些明确的例子。
Conformal classical Yang–Baxter equation and S -equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras. In this paper, they are interpreted in terms of a kind of operators, namely O -operators in the conformal sense. Explicitly, the skew-symmetric part of a conformal linear map T where T 0 = T λ | λ = 0 is an O -operator in the conformal sense is a skew-symmetric solution of conformal classical Yang–Baxter equation, whereas the symmetric part is a symmetric solution of conformal S -equation. One by-product is that a finite left-symmetric conformal algebra which is a free C [ ∂ ] -module gives a natural O -operator, and hence, there is a construction of solutions of conformal classical Yang–Baxter equation and conformal S -equation from the former. Another by-product is that the non-degenerate solutions of these two equations correspond to 2-cocycles of Lie conformal algebras and left-symmetric conformal algebras, respectively. We also give a further study on a special class of O -operators called Rota–Baxter operators on Lie conformal algebras, and some explicit examples are presented.