Authors: Askar Ali M.
Himadri Mukherjee
Đorđević, Bogdan 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Solutions to a system of Yang-Baxter matrix equations
Journal: Filomat
Volume: 38
Issue: 29
First page: 10169
Last page: 10192
Issue Date: 2024
Rank: M22
ISSN: 0354-5180
DOI: 10.2298/FIL2429169A
Abstract: 
n this article, a system of Yang-Baxter-type matrix equations is studied, XAX = BXB, XBX =
AXA, which “generalizes” the matrix Yang-Baxter equation and exhibits a broken symmetry. We investigate
the solutions of this system from various geometric and topological points of view. We analyze the existence
of doubly stochastic solutions and intertwining solutions to the system and describe the conditions for their
existence. Furthermore, we characterize the case when A and B are idempotent orthogonal complements.
i.e., A2 = A, B2 = B, AB = BA = 0. We also completely characterize the set of solutions for n = 2 using
commutative algebraic techniques
Publisher: Faculty of Sciences and Mathematics, University of Niš, Serbia
Project: The third author is supported by the Ministry of Science, Technological Development and Innovations, Republic of Serbia, grant No. 451-03-66/2024-03/200029, and by the bilateral project between the Republic of Serbia and France (Generalized inverses on algebraic structures and applications), grant no. 337-00-93/2022-05/13.

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