扭曲q- yangian和Sklyanin行列式

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-03 DOI:10.1112/jlms.70114

Naihuan Jing, Jian Zhang

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引用次数: 0

摘要

q$ q$ -Yangian既可以看作是上三角李代数的环代数的量子变形，也可以看作是Yangian代数的变形。本文研究了量子仿射代数是q$ q$ -Yangian代数的两个拷贝的乘积。这一观点使我们能够研究量子仿射代数及其扭曲版本的不变性理论。我们引入扭曲量子仿射代数的扭曲Sklyanin行列式，并证明它们在中心产生中心元素。我们还建立了Sklyanin行列式的各种恒等式。

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Twisted q-Yangians and Sklyanin determinants

$q$ -Yangians can be viewed both as quantum deformations of the loop algebras of upper triangular Lie algebras and deformations of the Yangian algebras. In this paper, we study the quantum affine algebra as a product of two copies of the $q$ -Yangian algebras. This viewpoint enables us to investigate the invariant theory of quantum affine algebras and their twisted versions. We introduce the twisted Sklyanin determinant for twisted quantum affine algebras and show that they generate central elements in the center. We also establish various identities for the Sklyanin determinants.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.