New constructions of Yang-Baxter systems
Florin F. Nichita, Deepak Parashar
TL;DR
This paper introduces new algebraic constructions of Yang-Baxter systems, expanding the types of solutions available and explicitly detailing the associated algebraic structures in low dimensions.
Contribution
It presents novel methods to construct both constant and spectral-parameter dependent Yang-Baxter systems from algebra structures.
Findings
New algebraic constructions of Yang-Baxter systems.
Explicit description of the commutation algebra in dimension two.
Extension of solutions to both constant and spectral-parameter dependent cases.
Abstract
The quantum Yang-Baxter equation admits generalisations to systems of Yang-Baxter type equations called Yang-Baxter systems. Starting from algebra structures, we propose new constructions of some constant as well as the spectral-parameter dependent Yang-Baxter systems. Besides, we also present explicitly the commutation algebra structure associated to the constant type in dimension two.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms