TL;DR
This paper introduces the rime Ansatz as a weakened form of the ice Ansatz for matrix solutions of the Yang-Baxter equation, classifies generic solutions, and relates them to known models like Cremmer-Gervais.
Contribution
It defines the rime Ansatz, describes generic solutions, and establishes their equivalence to Cremmer-Gervais solutions, expanding the understanding of Yang-Baxter solutions.
Findings
Rime solutions generalize ice solutions for Yang-Baxter matrices.
Non-unitary rime R-matrices are equivalent to Cremmer-Gervais solutions.
Classical r-matrices satisfy associative classical Yang-Baxter equations.
Abstract
The ice Ansatz on matrix solutions of the Yang-Baxter equation is weakened to a condition which we call rime. Generic rime solutions of the Yang-Baxter equation are described. We prove that the rime non-unitary (respectively, unitary) R-matrix is equivalent to the Cremmer-Gervais (respectively, boundary Cremmer-Gervais) solution. Generic rime classical r-matices satisfy the (non-)homogeneous associative classical Yang-Baxter equation.
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Taxonomy
TopicsCritical Theory and Philosophy · Seventeenth-Century Political and Philosophical Thought · Political Theology and Sovereignty