R-Matrix Formulation of the Quantum Inhomogeneous Groups Iso_qr(N) and Isp_qr(N)

Abstract

The quantum commutations $RTT=TTR$ and the orthogonal (symplectic) conditions for the inhomogeneous multiparametric $q$-groups of the $B_n,C_n,D_n$ type are found in terms of the $R$-matrix of $B_{n+1},C_{n+1},D_{n+1}$. A consistent Hopf structure on these inhomogeneous $q$-groups is constructed by means of a projection from $B_{n+1},C_{n+1},D_{n+1}$. Real forms are discussed: in particular we obtain the $q$-groups $IS{O}_{q,r}(n+1,n-1)$, including the quantum Poincaré group.

14 pages, latex, no figures

References in corpus (4)

• An introduction to non-commutative differential geometry on quantum groups
• Differential Calculus on Iso_q (N), Quantum Poincare' Algebra and q - Gravity
• Gauge theories of quantum groups
• R matrix and bicovariant calculus for the inhomogeneous quantum groups IGL_q(n)

Cited by in corpus (8)

• Noncommutative Geometry and Gravity
• Noncommutative Symmetries and Gravity
• Noncommutative principal bundles through twist deformation
• Universal Enveloping Algebra and Differential Calculi on Orthogonal q-groups
• Cayley--Klein Contractions of Quantum Orthogonal Groups in Cartesian Basis
• Deformation quantization of principal bundles
• On the Geometry of the Quantum Poincare Group
• On contractions of quantum orthogonal groups