Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Dancer, K. A."'
Publikováno v:
Nucl.Phys.B836:171-185,2010
The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld double D(D_
Externí odkaz:
http://arxiv.org/abs/1003.3514
Publikováno v:
Nuclear Physics B 847 [FS] (2011), 387--412
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as de
Externí odkaz:
http://arxiv.org/abs/1003.0501
Publikováno v:
Nucl. Phys. B, Vol. 812, no. 3 (2009) 456-469
A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where $R$-matrix solutions of the Yang--Baxter equation do not have the property of crossing unitarity. Suitably modified forms of the refle
Externí odkaz:
http://arxiv.org/abs/0811.1248
Autor:
Dancer, K. A., Links, J.
Two universal spectral parameter-dependent Lax operators are presented in terms of the elements of the Drinfeld double $D(D_3)$ of the dihedral group $D_3$. Applying representations of $D(D_3)$ to these yields matrix solutions of the Yang-Baxter equa
Externí odkaz:
http://arxiv.org/abs/0810.5601
Publikováno v:
J. Phys. A: Math. Theor. 40 F1069 (2007)
We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with $\mathbb{Z}$-graded Hopf algebras. To demonstrate the approach, we provide examples for the Taft algebras and the quantum group $U_q[sl(2)]$.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/0710.3628
We study the construction of premonoidal categories, where the pentagon relation fails, through representations of finite group algebras and their quantum doubles. Both finite group algebras and their quantum doubles have a finite number of irreducib
Externí odkaz:
http://arxiv.org/abs/math/0606704
Autor:
Dancer, K. A.
For the last fifteen years quantum superalgebras have been used to model supersymmetric quantum systems. A class of quasi-triangular Hopf superalgebras, they each contain a universal $R$-matrix, which automatically satisfies the Yang--Baxter equation
Externí odkaz:
http://arxiv.org/abs/math/0511426
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter equation. Such sol
Externí odkaz:
http://arxiv.org/abs/math/0511072
The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra $U_q[sl(m|n)]$, with a multipar
Externí odkaz:
http://arxiv.org/abs/nlin/0509019
Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on the vector
Externí odkaz:
http://arxiv.org/abs/math/0506387