Generalization of the U q (gl(N)) Algebra and Staggered Models

2001/06/15 by D. Arnaudon, A. Sedrakyan, T. Sedrakyan +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #cond-mat.str-el #hep-th

paper · pdf · doi:10.1023/a:1014504526934

published as Lett.Math.Phys. 58 (2001) 209-222 · 12 pages ; Latex2e

arxiv created 2001/06/15 · openalex publication_date 2001/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We develop a technique of construction of integrable models with a Z₂ grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter Equations are written down and their solution for the gl(N) case are found. We analyze in details the N=2 case and find the corresponding quantum group behind this solution. It can be regarded as quantum U_q,B(gl(2)) group with a matrix deformation parameter qB with (qB)²=q². The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of U_q(gl(N)) with a Cartan generator related to deformation parameter -1.

Citations

• THE QUANTUM METHOD OF THE INVERSE PROBLEM AND THE HEISENBERG XYZ MODEL
• Percolation, quantum tunnelling and the integer Hall effect

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