Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures

In our earlier article [Lett. Math. Phys. 107 (2017), 475-503], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every deformation quantization leads to a Drinfeld twist of the associative bialgebroid...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Authors: Meljanac, S., Škoda, Z.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209438
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures / S. Meljanac, Z. Škoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-209438
record_format dspace
spelling Meljanac, S.
Škoda, Z.
2025-11-21T18:52:03Z
2018
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures / S. Meljanac, Z. Škoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 53D55; 16S30; 16T05
arXiv: 1605.01376
https://nasplib.isofts.kiev.ua/handle/123456789/209438
https://doi.org/10.3842/SIGMA.2018.026
In our earlier article [Lett. Math. Phys. 107 (2017), 475-503], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every deformation quantization leads to a Drinfeld twist of the associative bialgebroid of h-adic series of differential operators on a fixed Poisson manifold. In the case of linear Poisson structures, the twisted bialgebroid essentially coincides with our construction. Using our explicit description of the Hopf algebroid, we compute the corresponding Drinfeld twist explicitly as a product of two exponential expressions.
S.M. has been supported by the Croatian Science Foundation under the Project no. IP-2014-09-9582 and the H2020 Twinning project no. 692194 “RBI-T-WINNING”. Z.Š. has been partly supported by grant no. 18-00496S of the Czech Science Foundation. We thank A. Borowiec for his remarks on the paper and M. Stojić for his remarks on Sections 1 and 2. We thank the referees for bringing to our attention numerous constructive suggestions, which helped extend and improve the article significantly.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
spellingShingle Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
Meljanac, S.
Škoda, Z.
title_short Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
title_full Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
title_fullStr Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
title_full_unstemmed Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
title_sort hopf algebroid twists for deformation quantization of linear poisson structures
author Meljanac, S.
Škoda, Z.
author_facet Meljanac, S.
Škoda, Z.
publishDate 2018
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description In our earlier article [Lett. Math. Phys. 107 (2017), 475-503], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every deformation quantization leads to a Drinfeld twist of the associative bialgebroid of h-adic series of differential operators on a fixed Poisson manifold. In the case of linear Poisson structures, the twisted bialgebroid essentially coincides with our construction. Using our explicit description of the Hopf algebroid, we compute the corresponding Drinfeld twist explicitly as a product of two exponential expressions.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/209438
citation_txt Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures / S. Meljanac, Z. Škoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ.
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first_indexed 2025-11-24T07:13:53Z
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