TY - JOUR
T1 - Universal enveloping algebra and differential calculi on inhomogeneous orthogonal q-groups
AU - Aschieri, Paolo
AU - Castellani, Leonardo
N1 - Funding Information:
The first author (PA) is supported by a joint fellowship University of California-Scuola Normale Superiore, Pisa, Italy and by Fondazione Angelo Della Riccia, Firenze, Italy. Part of this work has been accomplished through the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the US Department of Energy under Contract DE-AC03-76SF00098. Work supported in part by EEC under TMR contract FMRX-CT96-0045.
PY - 1998/7
Y1 - 1998/7
N2 - 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 Uq,r(iso(N)), characterized as the Hopf algebra of regular functionals on ISOq,r(N), is found as a Hopf subalgebra of Uq,r(so(N + 2)) and is shown to be a bicovariant bimodule over Uq,r(so(N)). An R-matrix formulation of Uq,r(iso(N)) is given and we prove the pairing Uq,r(so(N)) ↔ ISOq,r(N). We analyze the subspaces of Uq,r(iso(N)) that define bicovariant differential calculi on ISOq,r(N).
AB - 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 Uq,r(iso(N)), characterized as the Hopf algebra of regular functionals on ISOq,r(N), is found as a Hopf subalgebra of Uq,r(so(N + 2)) and is shown to be a bicovariant bimodule over Uq,r(so(N)). An R-matrix formulation of Uq,r(iso(N)) is given and we prove the pairing Uq,r(so(N)) ↔ ISOq,r(N). We analyze the subspaces of Uq,r(iso(N)) that define bicovariant differential calculi on ISOq,r(N).
KW - Bimodules
KW - Hopf algebra
KW - Multiparametric quantum groups
KW - Universal enveloping algebra
UR - http://www.scopus.com/inward/record.url?scp=0032119409&partnerID=8YFLogxK
U2 - 10.1016/S0393-0440(97)00045-4
DO - 10.1016/S0393-0440(97)00045-4
M3 - Article
SN - 0393-0440
VL - 26
SP - 247
EP - 271
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
IS - 3-4
ER -