Morita equivalence of formal Poisson structures
We extend the notion of Morita equivalence of Poisson manifolds to the setting of {\em formal} Poisson structures, i.e., formal power series of bivector fields $\pi=\pi_0 + \lambda\pi_1 +\cdots$ satisfying the Poisson integrability condition $[\pi,\pi]=0$. Our main result gives a complete descriptio...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Language: | English |
| Published: |
17-06-2020
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We extend the notion of Morita equivalence of Poisson manifolds to the
setting of {\em formal} Poisson structures, i.e., formal power series of
bivector fields $\pi=\pi_0 + \lambda\pi_1 +\cdots$ satisfying the Poisson
integrability condition $[\pi,\pi]=0$. Our main result gives a complete
description of Morita equivalent formal Poisson structures deforming the zero
structure ($\pi_0=0$) in terms of $B$-field transformations, relying on a
general study of formal deformations of Poisson morphisms and dual pairs.
Combined with previous work on Morita equivalence of star products, our results
link the notions of Morita equivalence in Poisson geometry and noncommutative
algebra via deformation quantization. |
|---|---|
| AbstractList | We extend the notion of Morita equivalence of Poisson manifolds to the
setting of {\em formal} Poisson structures, i.e., formal power series of
bivector fields $\pi=\pi_0 + \lambda\pi_1 +\cdots$ satisfying the Poisson
integrability condition $[\pi,\pi]=0$. Our main result gives a complete
description of Morita equivalent formal Poisson structures deforming the zero
structure ($\pi_0=0$) in terms of $B$-field transformations, relying on a
general study of formal deformations of Poisson morphisms and dual pairs.
Combined with previous work on Morita equivalence of star products, our results
link the notions of Morita equivalence in Poisson geometry and noncommutative
algebra via deformation quantization. |
| Author | Bursztyn, Henrique Ortiz, Inocencio Waldmann, Stefan |
| Author_xml | – sequence: 1 givenname: Henrique surname: Bursztyn fullname: Bursztyn, Henrique – sequence: 2 givenname: Inocencio surname: Ortiz fullname: Ortiz, Inocencio – sequence: 3 givenname: Stefan surname: Waldmann fullname: Waldmann, Stefan |
| BackLink | https://doi.org/10.48550/arXiv.2006.10240$$DView paper in arXiv |
| BookMark | eNotzr1uwjAUQGEP7dBSHoCpfoGE69jGzlih0lYKgoE9uvGPZCmJwU5Q-_aotNPZjr5n8jDG0RGyYlAKLSWsMX2Ha1kBbEoGlYAnst7HFCak7jKHK_ZuNI5GT31MA_b0GEPOcaR5SrOZ5uTyC3n02Ge3_O-CnHbvp-1n0Rw-vrZvTYEbBUWnDGpnFLNSKi28Ytqh0FzU3Bhe-4oBaMW4tcYKKzorre4UIID1YDjyBXn9297F7TmFAdNP-ytv73J-A6_4P-s |
| ContentType | Journal Article |
| Copyright | http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| Copyright_xml | – notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| DBID | AKZ GOX |
| DOI | 10.48550/arxiv.2006.10240 |
| DatabaseName | arXiv Mathematics arXiv.org |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| ExternalDocumentID | 2006_10240 |
| GroupedDBID | AKZ GOX |
| ID | FETCH-LOGICAL-a670-b7ca8ec71d55784f718ea483493cc39f21008713ddcd4d4bd5d8b70a00df0c3a3 |
| IEDL.DBID | GOX |
| IngestDate | Mon Jan 08 05:43:14 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a670-b7ca8ec71d55784f718ea483493cc39f21008713ddcd4d4bd5d8b70a00df0c3a3 |
| OpenAccessLink | https://arxiv.org/abs/2006.10240 |
| ParticipantIDs | arxiv_primary_2006_10240 |
| PublicationCentury | 2000 |
| PublicationDate | 2020-06-17 |
| PublicationDateYYYYMMDD | 2020-06-17 |
| PublicationDate_xml | – month: 06 year: 2020 text: 2020-06-17 day: 17 |
| PublicationDecade | 2020 |
| PublicationYear | 2020 |
| Score | 1.7736785 |
| SecondaryResourceType | preprint |
| Snippet | We extend the notion of Morita equivalence of Poisson manifolds to the
setting of {\em formal} Poisson structures, i.e., formal power series of
bivector fields... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Symplectic Geometry |
| Title | Morita equivalence of formal Poisson structures |
| URI | https://arxiv.org/abs/2006.10240 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV07T8MwED6RTiwIBKg85YHVauI4cTIiaOnCQ6JDt8qxz1Il1ABVED-_d04QLKy2l7Pv9fns7wBuLDpsKqektUZJjU7LilRHeo7u5BwzDPzfef5qnpbV_ZRpcsTPXxj7-b3-6vmBm-0k1goypuFKIFGKn2w9PC_74mSk4hrW_66jHDMO_QkSs0M4GLI7cdsfxxHs4eYYJo8tI3CBH92azpVNSbRBxGzxTby0JHq7ET2Ra0fo9wQWs-nibi6HPgXSliaVjXG2QmcyX5D660DeHi3f0dW5c3kdFPPnEBb03nntdeMLXzUmtWnqQ-pym5_CiKA-jkEwvV1ZYyjKkGss0CoyH9ovwglZQYnaGYyjdKv3noqCm0iWqyj4-f9TF7CvGCVyxx1zCSOSB68g2fruOu7nDs0McwQ |
| link.rule.ids | 228,230,782,887 |
| linkProvider | Cornell University |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Morita+equivalence+of+formal+Poisson+structures&rft.au=Bursztyn%2C+Henrique&rft.au=Ortiz%2C+Inocencio&rft.au=Waldmann%2C+Stefan&rft.date=2020-06-17&rft_id=info:doi/10.48550%2Farxiv.2006.10240&rft.externalDocID=2006_10240 |