Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions

1997/10/27 by Murray Gerstenhaber, Gerstenhaber, Murray, Anthony Giaquinto +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9710033

openalex publication_date 1997/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Boundary solutions to the quantum Yang-Baxter (qYB) equation are defined to be those in the boundary of (but not in) the variety of solutions to the ``modified'' qYB equation, the latter being analogous to the modified classical Yang-Baxter (cYB) equation. We construct, for a large class of solutions r to the modified cYB equation, explicit ``boundary quantizations'', i.e., boundary solutions to the qYB equation of the form I+tr+ t²r₂ + .... In the last section we list and give quantizations for all classical r-matrices in sl(3) \wedge sl(3).

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