R-matrix formulation of the quantum inhomogeneous groups ISOq,r(N) and ISpq,r(N)
Abstract
The quantum commutationsRTT=TTR and the orthogonal (symplectic) conditions for the inhomogeneous multiparametricq-groups of theBn,Cn,Dntype are found in terms of theR-matrix ofBn+1,Cn+1,Dn+1.A consistent Hopf structure on these inhomogeneousq-groups is constructed by means of a projection fromBn+1,Cn+1,Dn+1.Real forms are discussed; in particular, we obtain theq-groups ISOq,r(n+1,n-1), including the quantum Poincaré group. The inhomogeneusq-groups do not contain dilatations when the parameters satisfy certain conditions. For example, we find a dilatation-freeq-Poincaré group depending on one real parameterq.
- Publication:
-
Letters in Mathematical Physics
- Pub Date:
- February 1996
- DOI:
- arXiv:
- arXiv:hep-th/9411039
- Bibcode:
- 1996LMaPh..36..197A
- Keywords:
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- 81R50;
- 16W30;
- 22E70;
- Multi parametric quantum inhomogeneous groups;
- quantum Poincaré groups;
- quotient Hopf algebras;
- High Energy Physics - Theory
- E-Print:
- 14 pages, latex, no figures