ar X iv : q - a lg / 9 51 10 16 v 2 2 8 N ov 1 99 5 Solution of constant Yang – Baxter system in the dimension two
نویسنده
چکیده
The quantised braided groups were introduced recently in [1] combining Majid’s concept of braided groups [2] and the FRT formulation of quantum supergroups [3]. The generators of quantised braided groups T = T j i , i, j ∈ {1, . . . , d = dimV } satisfy the algebraic and braid relations Q12R −1 12 T1R12T2 = R −1 21 T2R21T1Q12 (1) ψ(T1 ⊗R12T2) = R12T2 ⊗R −1 12 T1R12 (2) where the numerical matrices Q, R satisfy the system of Yang–Baxter–type equations Q12Q13Q23 = Q23Q13Q12, (3) R12R13R23 = R23R13R12, (4) Q12R13R23 = R23R13Q12, (5) R12R13Q23 = Q23R13R12. (6) The special cases of the quantised braided groups are the quantum supergroups [3], quantum anyonic groups [4] and braided GLq groups [5]. ∗Postal address: Břehová 7, 115 19 Prague 1, Czech Republic. E-mail: [email protected]
منابع مشابه
ar X iv : q - a lg / 9 71 10 27 v 1 2 8 N ov 1 99 7 Yang – Baxter systems , solutions and applications
Two types of Yang–Baxter systems play roles in the theoretical physics – constant and colour dependent. The constant systems are used mainly for construction of special Hopf algebra while the colour or spectral dependent for construction of quantum integrable models. Examples of both types together with their particular solutions are presented. The complete solution is known only for the consta...
متن کاملar X iv : q - a lg / 9 70 50 27 v 1 2 8 M ay 1 99 7 Jordanian U h , s gl ( 2 ) and its coloured realization
A two-parametric non-standard (Jordanian) deformation of the Lie algebra gl(2) is constructed, and then, exploited to obtain a new, triangular R-matrix solution of the coloured Yang-Baxter equation. The corresponding coloured quantum group is presented explicitly.
متن کاملar X iv : q - a lg / 9 51 10 02 v 1 2 N ov 1 99 5 Phase spaces related to standard classical r - matrices
Fundamental representations of real simple Poisson Lie groups are Poisson actions with a suitable choice of the Poisson structure on the underlying (real) vector space. We study these (mostly quadratic) Poisson structures and corresponding phase spaces (symplectic groupoids).
متن کاملar X iv : q - a lg / 9 51 10 18 v 1 2 3 N ov 1 99 5 Unitary operator bases and q - deformed algebras
Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commu-tation relation is shown to emerge in a natural way, when the deformation parameter is a root of unity.
متن کاملar X iv : q - a lg / 9 70 50 22 v 1 2 7 M ay 1 99 7 Coloured Hopf
Some new algebraic structures related to the coloured Yang-Baxter equation, and termed coloured Hopf algebras, are reviewed. Coloured quantum universal enveloping algebras of Lie algebras are defined in this context. An extension to the coloured graded Yang-Baxter equation and coloured Hopf superalgebras is also presented. The coloured two-parameter quantum universal enveloping algebra of gl(1/...
متن کامل