Euclidean and super euclidean algebras and localizations of Uq (sl(2)) and Uq(osp(1j2))1

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

In Ref. 1 we described homomorphisms of Uq((2)) and U((2)) into localizations of U((2)) and Uq((2)), respectively, with U((2)) being the universal enveloping algebra of the Lie algebra of SO(2) × sT2 the Euclidean group in the plane, with T2 denoting translations of the plane and × s semidirect product. In particular, we obtained explicit expressions for the generators of U q((2)) and U((2)), respectively as irrational functions of U((2)) and Uq((2)). Herewith we further develop our results extending them to Uq((1|2)) and U ) with being the super Euclidean algebra.

Original languageEnglish (US)
Article number012026
JournalJournal of Physics: Conference Series
Volume512
Issue number1
DOIs
StatePublished - Jan 1 2014
Event8th International Symposium on Quantum Theory and Symmetries, QTS 2013 - Mexico City, Mexico
Duration: Aug 5 2013Aug 9 2013

Fingerprint

algebra
homomorphisms
generators
products

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

@article{46190a2410d54945a7517dc772216896,
title = "Euclidean and super euclidean algebras and localizations of Uq (sl(2)) and Uq(osp(1j2))1",
abstract = "In Ref. 1 we described homomorphisms of Uq((2)) and U((2)) into localizations of U((2)) and Uq((2)), respectively, with U((2)) being the universal enveloping algebra of the Lie algebra of SO(2) × sT2 the Euclidean group in the plane, with T2 denoting translations of the plane and × s semidirect product. In particular, we obtained explicit expressions for the generators of U q((2)) and U((2)), respectively as irrational functions of U((2)) and Uq((2)). Herewith we further develop our results extending them to Uq((1|2)) and U ) with being the super Euclidean algebra.",
author = "Moylan, {Patrick J.}",
year = "2014",
month = "1",
day = "1",
doi = "10.1088/1742-6596/512/1/012026",
language = "English (US)",
volume = "512",
journal = "Journal of Physics: Conference Series",
issn = "1742-6588",
publisher = "IOP Publishing Ltd.",
number = "1",

}

Euclidean and super euclidean algebras and localizations of Uq (sl(2)) and Uq(osp(1j2))1. / Moylan, Patrick J.

In: Journal of Physics: Conference Series, Vol. 512, No. 1, 012026, 01.01.2014.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Euclidean and super euclidean algebras and localizations of Uq (sl(2)) and Uq(osp(1j2))1

AU - Moylan, Patrick J.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In Ref. 1 we described homomorphisms of Uq((2)) and U((2)) into localizations of U((2)) and Uq((2)), respectively, with U((2)) being the universal enveloping algebra of the Lie algebra of SO(2) × sT2 the Euclidean group in the plane, with T2 denoting translations of the plane and × s semidirect product. In particular, we obtained explicit expressions for the generators of U q((2)) and U((2)), respectively as irrational functions of U((2)) and Uq((2)). Herewith we further develop our results extending them to Uq((1|2)) and U ) with being the super Euclidean algebra.

AB - In Ref. 1 we described homomorphisms of Uq((2)) and U((2)) into localizations of U((2)) and Uq((2)), respectively, with U((2)) being the universal enveloping algebra of the Lie algebra of SO(2) × sT2 the Euclidean group in the plane, with T2 denoting translations of the plane and × s semidirect product. In particular, we obtained explicit expressions for the generators of U q((2)) and U((2)), respectively as irrational functions of U((2)) and Uq((2)). Herewith we further develop our results extending them to Uq((1|2)) and U ) with being the super Euclidean algebra.

UR - http://www.scopus.com/inward/record.url?scp=84902362459&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902362459&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/512/1/012026

DO - 10.1088/1742-6596/512/1/012026

M3 - Conference article

AN - SCOPUS:84902362459

VL - 512

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012026

ER -