The Yang-Baxter matrix equation for involutions

Miskolc Mathematical Notes

article

Ryszard R. Andruszkiewicz¹  Alicja Smoktunowicz² 

[1] Faculty of Mathematics, University of Białystok;Faculty of Mathematics and Information Science, Warsaw University of Technology

关键词: Yang-Baxter equation;    involution;    eigenvalues;    quadratic matrices;   

DOI  :  10.18514/MMN.2022.3761

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

In this paper we find all involutive solutions $X \in \mathbb C^{n \times n}$ of the Yang-Baxter matrix equation $AXA=XAX$, where $A \in \mathbb C^{n \times n}$ is a given involutory matrix. The construction is algorithmic. It is based on the concept of quadratic matrices. Algorithms for generating concrete involutive solutions of the Yang-Baxter matrix equation $AXA=XAX$ are also presented along with several examples.

【 授权许可】

CC BY