Localizations of uq(si(2)) and uq(osp(1/2)) associated with euclidean and super euclidean algebras

Patrick Moylan

doi:10.1007/978-4-431-55285-7_27

Localizations of u_q(si(2)) and u_q(osp(1/2)) associated with euclidean and super euclidean algebras

Patrick Moylan

Division of Engineering and Science (Abington)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

We construct homomorphisms from the Euclidean and super Euclidean algebras, iso(2) and (Formual presented), onto their images in localizations of U_q(sl(2)) and U_q(osp(1|2)), respectively, and, conversely, we describe homomorphisms of U_q(sl(2)) and U_q(osp(1|2)) into localizations of U(iso(2)) and (Formual presented). These homomorphisms give results on the relationship between the representation theory of the respective algebras, and, in particular, lead to new representations of U_q(osp(1|2)).

Original language	English (US)
Title of host publication	Lie Theory and Its Applications in Physics, 2013
Editors	Vladimir Dobrev
Publisher	Springer New York LLC
Pages	369-379
Number of pages	11
ISBN (Electronic)	9784431552840
DOIs	https://doi.org/10.1007/978-4-431-55285-7_27
State	Published - Jan 1 2014
Event	10th Workshop on Lie Theory and Its Applications in Physics, LT 2013 - , Bulgaria Duration: Jun 17 2013 → Jun 23 2013

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	111
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	10th Workshop on Lie Theory and Its Applications in Physics, LT 2013
Country/Territory	Bulgaria
Period	6/17/13 → 6/23/13

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/978-4-431-55285-7_27

Cite this

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title = "Localizations of uq(si(2)) and uq(osp(1/2)) associated with euclidean and super euclidean algebras",

abstract = "We construct homomorphisms from the Euclidean and super Euclidean algebras, iso(2) and (Formual presented), onto their images in localizations of Uq(sl(2)) and Uq(osp(1|2)), respectively, and, conversely, we describe homomorphisms of Uq(sl(2)) and Uq(osp(1|2)) into localizations of U(iso(2)) and (Formual presented). These homomorphisms give results on the relationship between the representation theory of the respective algebras, and, in particular, lead to new representations of Uq(osp(1|2)).",

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Moylan, P 2014, Localizations of u_q(si(2)) and u_q(osp(1/2)) associated with euclidean and super euclidean algebras. in V Dobrev (ed.), Lie Theory and Its Applications in Physics, 2013. Springer Proceedings in Mathematics and Statistics, vol. 111, Springer New York LLC, pp. 369-379, 10th Workshop on Lie Theory and Its Applications in Physics, LT 2013, Bulgaria, 6/17/13. https://doi.org/10.1007/978-4-431-55285-7_27

Localizations of u_q(si(2)) and u_q(osp(1/2)) associated with euclidean and super euclidean algebras. / Moylan, Patrick.
Lie Theory and Its Applications in Physics, 2013. ed. / Vladimir Dobrev. Springer New York LLC, 2014. p. 369-379 (Springer Proceedings in Mathematics and Statistics; Vol. 111).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - We construct homomorphisms from the Euclidean and super Euclidean algebras, iso(2) and (Formual presented), onto their images in localizations of Uq(sl(2)) and Uq(osp(1|2)), respectively, and, conversely, we describe homomorphisms of Uq(sl(2)) and Uq(osp(1|2)) into localizations of U(iso(2)) and (Formual presented). These homomorphisms give results on the relationship between the representation theory of the respective algebras, and, in particular, lead to new representations of Uq(osp(1|2)).

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