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Article: On the Standard Poisson Structure and a Frobenius Splitting of the Basic Affine Space

TitleOn the Standard Poisson Structure and a Frobenius Splitting of the Basic Affine Space
Authors
Issue Date2019
PublisherOxford University Press. The Journal's web site is located at http://imrn.oxfordjournals.org
Citation
International Mathematics Research Notices, 2019, Epub 2019-08-02 How to Cite?
AbstractThe goal of this paper is to construct a Frobenius splitting on G/U via the Poisson geometry of (G/U,πG/U)⁠, where G is a simply connected semi-simple algebraic group defined over an algebraically closed field of characteristic p>3⁠, U is the uniradical of a Borel subgroup of G⁠, and πG/U is the standard Poisson structure on G/U⁠. We first study the Poisson geometry of (G/U,πG/U)⁠. Then we develop a general theory for Frobenius splittings on T-Poisson varieties, where T is an algebraic torus. In particular, we prove that compatibly split subvarieties of Frobenius splittings constructed in this way must be T-Poisson subvarieties. Lastly, we apply our general theory to construct a Frobenius splitting on G/U⁠.
Persistent Identifierhttp://hdl.handle.net/10722/282004
ISSN
2019 Impact Factor: 1.291
2015 SCImago Journal Rankings: 2.052

 

DC FieldValueLanguage
dc.contributor.authorPENG, J-
dc.contributor.authorYu, S-
dc.date.accessioned2020-04-19T03:34:00Z-
dc.date.available2020-04-19T03:34:00Z-
dc.date.issued2019-
dc.identifier.citationInternational Mathematics Research Notices, 2019, Epub 2019-08-02-
dc.identifier.issn1073-7928-
dc.identifier.urihttp://hdl.handle.net/10722/282004-
dc.description.abstractThe goal of this paper is to construct a Frobenius splitting on G/U via the Poisson geometry of (G/U,πG/U)⁠, where G is a simply connected semi-simple algebraic group defined over an algebraically closed field of characteristic p>3⁠, U is the uniradical of a Borel subgroup of G⁠, and πG/U is the standard Poisson structure on G/U⁠. We first study the Poisson geometry of (G/U,πG/U)⁠. Then we develop a general theory for Frobenius splittings on T-Poisson varieties, where T is an algebraic torus. In particular, we prove that compatibly split subvarieties of Frobenius splittings constructed in this way must be T-Poisson subvarieties. Lastly, we apply our general theory to construct a Frobenius splitting on G/U⁠.-
dc.languageeng-
dc.publisherOxford University Press. The Journal's web site is located at http://imrn.oxfordjournals.org-
dc.relation.ispartofInternational Mathematics Research Notices-
dc.rightsPre-print: Journal Title] ©: [year] [owner as specified on the article] Published by Oxford University Press [on behalf of xxxxxx]. All rights reserved. Pre-print (Once an article is published, preprint notice should be amended to): This is an electronic version of an article published in [include the complete citation information for the final version of the Article as published in the print edition of the Journal.] Post-print: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [insert journal title] following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: xxxxxxx [insert URL that the author will receive upon publication here].-
dc.titleOn the Standard Poisson Structure and a Frobenius Splitting of the Basic Affine Space-
dc.typeArticle-
dc.identifier.emailYu, S: yuszmath@hku.hk-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1093/imrn/rnz179-
dc.identifier.hkuros309715-
dc.identifier.volumeEpub 2019-08-02-
dc.publisher.placeUnited Kingdom-
dc.identifier.issnl1073-7928-

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