Multiparameter R-matrices and their quantum groups

Differential calculus on the quantum superspace and deformation of phase space

“…Note that for the case of GL(2|0) (GL(n|0)), (2.20) reduces to the well-known result forR-matrix of the 2-parameter (the multiparameter) deformation of GL (2) [11] (GL(n) [12,13]). (The multiparameter deformation of GL(n) was also considered in ref.…”

“…We now extend the differential calculus on quantum space developed by Wess and Zumino [10] and others [11][12][13][14] to this quantum superspace. Here we require that the exterior derivative d given by…”

LIE ALGEBRA OF THE q-POINCARÉ GROUP AND q-HEISENBERG COMMUTATION RELATIONS

“…These matrices are antidiagonal; they are equal, and for example for N = 4 they read C 14 = r −1 , C 23 = 1, C 32 = 1 and C 41 = r. The explicit expression of R and C is given in Ref. 6, (see the first reference in Ref. 10 for our notational conventions).…”

“…In the following we briefly define orthogonal quantum groups 5,6 and study their real forms. We see that there are two different conjugations that give two different quantum SO (3,1).…”

R-matrix formulation of the quantum inhomogeneous groups ISO q,r (N) and ISp q,r (N)

“…Then q ab → 1, r → 1 is the classical limit for which R ab cd → δ a c δ b d : the matrix entries T a b commute and become the usual entries of the fundamental representation. The multiparametric R matrices for the A, B, C, D series can be found in [10] (other ref.s on multiparametric q-groups are given in [11,12]). For the B, C, D case they read:…”