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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