Solving the two-dimensional constant quantum Yang-Baxter equation
May, 199237 pages
Published in:
- J.Math.Phys. 34 (1993) 1725-1756
DOI:
Report number:
- TURKU-FL-R7
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Abstract: (AIP)
A detailed analysis of the constant quantum Yang–Baxter equation R k 1 k 2 j 1 j 2 R l 1 k 3 k 1 j 3 R l 2 l 3 k 2 k 3 = R k 2 k 3 j 2 j 3 R k 1 l 3 j 1 k 3 R l 1 l 2 k 1 k 2 in two dimensions is presented, leading to an exhaustive list of its solutions. The set of 64 equations for 16 unknowns was first reduced by hand to several subcases which were then solved by computer using the Gröbner‐basis methods. Each solution was then transformed into a canonical form (based on the various trace matrices of R) for final elimination of duplicates and subcases. If we use homogeneous parametrization the solutions can be combined into 23 distinct cases, modulo the well‐known C, P, and T reflections, and rotations and scalings R̃=κ(Q⊗Q)R(Q⊗Q)−1.References(6)
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