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

Paolo Aschieri; Leonardo Castellani

doi:10.1016/S0393-0440(97)00045-4

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

Paolo Aschieri
, Leonardo Castellani

Research output: Contribution to journal › Article › peer-review

Abstract

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 Uq,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(so(N)) ↔ ISO_q,r(N). We analyze the subspaces of U_q,r(iso(N)) that define bicovariant differential calculi on ISO_q,r(N).

Original language	English
Pages (from-to)	247-271
Number of pages	25
Journal	Journal of Geometry and Physics
Volume	26
Issue number	3-4
DOIs	https://doi.org/10.1016/S0393-0440(97)00045-4
Publication status	Published - Jul 1998
Externally published	Yes

Keywords

Bimodules
Hopf algebra
Multiparametric quantum groups
Universal enveloping algebra

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10.1016/S0393-0440(97)00045-4

Cite this

@article{c3c6eca00a224d60ad769ac00012ce39,

title = "Universal enveloping algebra and differential calculi on inhomogeneous orthogonal q-groups",

abstract = "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).",

keywords = "Bimodules, Hopf algebra, Multiparametric quantum groups, Universal enveloping algebra",

author = "Paolo Aschieri and Leonardo Castellani",

note = "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.",

year = "1998",

month = jul,

doi = "10.1016/S0393-0440(97)00045-4",

language = "English",

volume = "26",

pages = "247--271",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier B.V.",

number = "3-4",

}

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 - https://www.scopus.com/pages/publications/0032119409

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 -

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

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Keywords

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