On the projection-based commuting solutions of the Yang-Baxter matrix equation

DOI10.1016/j.aml.2017.12.009zbMath1459.15021OpenAlexW2779769628MaRDI QIDQ1996396

Duanmei Zhou, Gaohang Yu, Jian Zhong, Guo-Liang Chen

Publication date: 4 March 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2017.12.009

zbMATH Keywords

eigenvaluesprojectionYang-Baxter equationJordan form

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Canonical forms, reductions, classification (15A21) Yang-Baxter equations (16T25) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items (6)

Constructing solutions of the Yang-Baxter-like matrix equation for singular matrices ⋮ Yang-Baxter-Like Matrix Equation: A Road Less Taken ⋮ Spectral properties of solutions of the Yang-Baxter-like matrix equation ⋮ Some non-commuting solutions of the Yang-Baxter-like matrix equation ⋮ On the intrinsic structure of the solution set to the Yang-Baxter-like matrix equation ⋮ All solutions of the Yang-Baxter-like matrix equation for nilpotent matrices of index two

Cites Work

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• Solving the Yang-Baxter-like matrix equation for rank-two matrices
• Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity
• On the Yang-Baxter-like matrix equation for rank-two matrices
• All solutions of the Yang-Baxter-like matrix equation for rank-one matrices
• Spectral solutions of the Yang-Baxter matrix equation
• Complete commuting solutions of the Yang-Baxter-like matrix equation for diagonalizable matrices
• Commuting solutions of the Yang-Baxter matrix equation
• On the structure of the spectral solutions of the Yang-Baxter matrix equation
• Partition function of the eight-vertex lattice model
• Further Solutions of a Yang-Baxter-like Matrix Equation
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

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