On constant Uq(sl2)-invariant R-matrices

  title={On constant Uq(sl2)-invariant R-matrices},
  author={Andrei G. Bytsko},
  journal={Journal of Mathematical Sciences},
  • A. Bytsko
  • Published 10 March 2010
  • Mathematics
  • Journal of Mathematical Sciences
We consider the spectral resolution of a Uq (sl2)-invariant solution R of the constant Yang–Baxter equation in the braid group form. It is shown that if the two highest coefficients in this resolution are not equal, then R is either the Drinfeld R-matrix or its inverse. Bibliography: 13 titles. 


An ansatz for sl2-invariant R-matrices
We study spectral decomposition of regular sl2-invariant R-matrices R(λ) by the method of reduction of the Yang-Baxter equation to subspaces of a given spin. Restrictions on the possible structure of
Quantum Groups
Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups
Quantum linear problem for the sine-Gordon equation and higher representations
A quantum linear problem is constructed which permits the investigation of the sine-Gordon equation within the framework of the inverse scattering method in an arbitrary representation of algebra.
Braids, link polynomials and a new algebra
A class function on the braid group is derived from the Kauffman link invariant. This function is used to construct representations of the braid groups depending on 2 parameters. The decomposition of
Yang-Baxter Relations in Terms of n-j Symbols of suq(2) Algebra
A trigonometric function parametrization of Yang-Baxter (Y-B) relations is described in terms of n - j symbols of su q (2), a deformation of su (2). The formalism starts with deduction of the Y-B
Non-Hermitian spin chains with inhomogeneous coupling
An open U_q(sl_2)-invariant spin chain of spin S and length N with inhomogeneous coupling is investigated as an example of a non-Hermitian (quasi-Hermitian) model. For several particular cases of
Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
  • H. Temperley, E. Lieb
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1971
A transfer-matrix approach is introduced to calculate the 'Whitney polynomial’ of a planar lattice, which is a generalization of the ‘percolation’ and ‘colouring’ problems. This new approach turns