Universal Enveloping Algebra and Differential Calculi on Orthogonal q-groups

Details Universal Enveloping Algebra and Differential Calculi on Orthogonal q-groups Universal Enveloping Algebra and Differential Calculi on Orthogonal q-groups

1997-05-27

arxiv.org/abs/q-alg/9705023v1

J.Geom.Phys. 26 (1998) 247-271

Mathematics

Quantum Algebra

LaTeX, 25 pages

Scientific paper

10.1016/S0393-0440(97)00045-4

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

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