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Article: On the Standard Poisson Structure and a Frobenius Splitting of the Basic Affine Space
| Title | On the Standard Poisson Structure and a Frobenius Splitting of the Basic Affine Space |
|---|---|
| Authors | |
| Issue Date | 2021 |
| Publisher | Oxford University Press. The Journal's web site is located at http://imrn.oxfordjournals.org |
| Citation | International Mathematics Research Notices, 2021, v. 2021 n. 15, p. 11618-11651 How to Cite? |
| Abstract | The 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 Identifier | http://hdl.handle.net/10722/282004 |
| ISSN | 2021 Impact Factor: 1.530 2020 SCImago Journal Rankings: 1.757 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | PENG, J | - |
| dc.contributor.author | Yu, S | - |
| dc.date.accessioned | 2020-04-19T03:34:00Z | - |
| dc.date.available | 2020-04-19T03:34:00Z | - |
| dc.date.issued | 2021 | - |
| dc.identifier.citation | International Mathematics Research Notices, 2021, v. 2021 n. 15, p. 11618-11651 | - |
| dc.identifier.issn | 1073-7928 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/282004 | - |
| dc.description.abstract | The 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.language | eng | - |
| dc.publisher | Oxford University Press. The Journal's web site is located at http://imrn.oxfordjournals.org | - |
| dc.relation.ispartof | International Mathematics Research Notices | - |
| dc.rights | Pre-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.title | On the Standard Poisson Structure and a Frobenius Splitting of the Basic Affine Space | - |
| dc.type | Article | - |
| dc.identifier.email | Yu, S: yuszmath@hku.hk | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1093/imrn/rnz179 | - |
| dc.identifier.hkuros | 309715 | - |
| dc.identifier.volume | Epub 2019-08-02 | - |
| dc.identifier.volume | 2021 | - |
| dc.identifier.issue | 15 | - |
| dc.identifier.spage | 11618 | - |
| dc.identifier.epage | 11651 | - |
| dc.identifier.isi | WOS:000739840200013 | - |
| dc.publisher.place | United Kingdom | - |
| dc.identifier.issnl | 1073-7928 | - |