MMN-3761

# The Yang-Baxter matrix equation for involutions

• Ryszard R. Andruszkiewicz, Faculty of Mathematics, University of Bialystok, Ciolkowskiego 1 M, 15-245 Bialystok, Poland, randrusz@math.uwb.edu.pl
• Alicja Smoktunowicz, Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland, A.Smoktunowicz@mini.pw.edu.pl

## Abstract

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.

Vol. 23 (2022), No. 1, pp. 61-70
DOI: 10.18514/MMN.2022.3761