Tetrahedron equation and generalized quantum groups
نویسندگان
چکیده
منابع مشابه
Zamolodchikov’s Tetrahedron Equation and Hidden Structure of Quantum Groups
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not related to the size of the lattice, therefore the same solution of the tetrahedron equation defines different integrable models for different finite periodic cubi...
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A generalized tetrahedron group is defined to be a group admitting the following presentation: 〈x, y, z | x = y = z = W p 1 (x, y) = W q 2 (y, z) = W r 3 (x, z) = 1〉, 2 ≤ l,m, n, p, q, r, where each Wi(a, b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized tri...
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A generalized tetrahedron group is defined to be a group admitting the following presentation: 〈x, y, z | xl = ym = zn = W p 1 (x, y) = W q 2 (y, z) = W r 3 (x, z) = 1〉, 2 ≤ l, m, n, p, q, r, where each Wi(a, b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized...
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The solvability of many 2d lattice statistical models is closely connected to the Quantum Yang-Baxter equation (QYBE) [1, 2]. Solutions of the QYBE are equivalent to weight functions of vertex models. Probably the most simple 2d integrable system is (lattice) gauge theory. The weights of the field configurations around a plaquette satisfy the QYBE Fig.1a. (The gauge group is assumed to be finit...
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We study numerically the dynamic and spectral properties of a one-dimensional quasi-periodic system, where site energies are given by k = V cos 2πf xk with xk denoting the kth quasiperiodic lattice site. When 2πf is given by the reciprocal lattice vector G(m, n) with n and m being successive Fibonacci numbers, the variance of the wavepacket is found to grow quadratically in time, regardless of ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2015
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/48/30/304001