κ-Deformed Phase Space, Hopf Algebroid and Twisting

Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion o...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2014
Автори: Jurić, T., Kovačević, D., Meljanac, S.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2014
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/146538
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:κ-Deformed Phase Space, Hopf Algebroid and Twisting / T. Jurić, D. Kovačević, S. Meljanac // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Jurić, T.
Kovačević, D.
Meljanac, S.
author_facet Jurić, T.
Kovačević, D.
Meljanac, S.
citation_txt κ-Deformed Phase Space, Hopf Algebroid and Twisting / T. Jurić, D. Kovačević, S. Meljanac // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for κ-deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of κ-Poincaré algebra. Several examples of realizations are worked out in details.
first_indexed 2025-11-25T23:46:46Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-11-25T23:46:46Z
publishDate 2014
publisher Інститут математики НАН України
record_format dspace
spelling Jurić, T.
Kovačević, D.
Meljanac, S.
2019-02-09T20:58:50Z
2019-02-09T20:58:50Z
2014
κ-Deformed Phase Space, Hopf Algebroid and Twisting / T. Jurić, D. Kovačević, S. Meljanac // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81R60; 17B37; 81R50
DOI:10.3842/SIGMA.2014.106
https://nasplib.isofts.kiev.ua/handle/123456789/146538
Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for κ-deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of κ-Poincaré algebra. Several examples of realizations are worked out in details.
This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
 full collection is available at http://www.emis.de/journals/SIGMA/space-time.html.
 The authors would like to thank A. Borowiec, J. Lukierski, A. Pachol, R. Strajn and Z. ˇ Skoda for ˇ
 useful discussions and comments. The authors would also like to thank the anonymous referee
 for useful comments and suggestions.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
κ-Deformed Phase Space, Hopf Algebroid and Twisting
Article
published earlier
spellingShingle κ-Deformed Phase Space, Hopf Algebroid and Twisting
Jurić, T.
Kovačević, D.
Meljanac, S.
title κ-Deformed Phase Space, Hopf Algebroid and Twisting
title_full κ-Deformed Phase Space, Hopf Algebroid and Twisting
title_fullStr κ-Deformed Phase Space, Hopf Algebroid and Twisting
title_full_unstemmed κ-Deformed Phase Space, Hopf Algebroid and Twisting
title_short κ-Deformed Phase Space, Hopf Algebroid and Twisting
title_sort κ-deformed phase space, hopf algebroid and twisting
url https://nasplib.isofts.kiev.ua/handle/123456789/146538
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AT meljanacs κdeformedphasespacehopfalgebroidandtwisting