Universal enveloping algebra and differential calculi on inhomogeneous orthogonal q-groups

JOURNAL OF GEOMETRY AND PHYSICS

卷:26

Article

Aschieri, P ; Castellani, L

关键词: multiparametric quantum groups;    universal enveloping algebra;    Hopf algebra;    bimodules;   

DOI  :  10.1016/S0393-0440(97)00045-4

来源: Elsevier

【 摘 要 】

We review the construction of the multiparametric quantum group ISOq,r(N) as a projection from SOq,r(N + 2) and show that it is a bicovariant bimodule over SOq,r(N). The universal enveloping algebra U-q,U-r(iso(N)), characterized as the Hopf algebra of regular functionals on ISOq,r(N), is found as a Hopf subalgebra of U-q,U-r(so(N + 2)) and is shown to be a bicovariant bimodule over U-q,U-r(so(N)). An R-matrix formulation of U-q,U-r(iso(N)) is given and we prove the pairing U-q,U-r(iso(N)) <-> ISOq,r(N). We analyze the subspaces of U-q,U-r(iso(N)) that define bicovariant differential calculi on ISOq,r(N).

【 授权许可】

Free