TY - JOUR
T1 - R-Matrix Formulation of the Quantum Inhomogeneous Groups ISOq,r(N) and ISpq,r(N)
AU - Aschieri, Paolo
AU - Castellani, Leonardo
PY - 1996
Y1 - 1996
N2 - The quantum commutations RTT = TTR and the orthogonal (symplectic) conditions for the inhomogeneous multiparametric q-groups of the Bn,Cn, Dn type are found in terms of the R-matrix of Bn+1, Cn+1, Dn+1. A consistent Hopf structure on these inhomogeneous q-groups is constructed by means of a projection from Bn+1,Cn+1, Dn+1. Real forms are discussed; in particular, we obtain the q-groups ISOq,r(n + 1, n - 1), including the quantum Poincaré group. The inhomogeneous q-groups do not contain dilatations when the parameters satisfy certain conditions. For example, we find a dilatation-free q-Poincaré group depending on one real parameter q.
AB - The quantum commutations RTT = TTR and the orthogonal (symplectic) conditions for the inhomogeneous multiparametric q-groups of the Bn,Cn, Dn type are found in terms of the R-matrix of Bn+1, Cn+1, Dn+1. A consistent Hopf structure on these inhomogeneous q-groups is constructed by means of a projection from Bn+1,Cn+1, Dn+1. Real forms are discussed; in particular, we obtain the q-groups ISOq,r(n + 1, n - 1), including the quantum Poincaré group. The inhomogeneous q-groups do not contain dilatations when the parameters satisfy certain conditions. For example, we find a dilatation-free q-Poincaré group depending on one real parameter q.
KW - Multi parametric quantum inhomogeneous groups
KW - Quantum poincaré groups
KW - Quotient hopf algebras
UR - http://www.scopus.com/inward/record.url?scp=0001744363&partnerID=8YFLogxK
U2 - 10.1007/BF00714382
DO - 10.1007/BF00714382
M3 - Article
SN - 0377-9017
VL - 36
SP - 197
EP - 211
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 2
ER -