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Article: Bott–samelson Varieties And Poisson Ore Extensions
Title | Bott–samelson Varieties And Poisson Ore Extensions |
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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. 14, p. 10745-10797 How to Cite? |
Abstract | We show that associated with any n-dimensional Bott–Samelson variety of a complex semi-simple Lie group G, one has 2n Poisson brackets on the polynomial algebra A=C[z1,…,zn], each an iterated Poisson Ore extension and one of them a symmetric Poisson Cauchon–Goodearl–Letzter (CGL) extension in the sense of Goodearl–Yakimov. We express the Poisson brackets in terms of root strings and structure constants of the Lie algebra of G. It follows that the coordinate rings of all generalized Bruhat cells have presentations as symmetric Poisson CGL extensions. The paper establishes the foundation on generalized Bruhat cells and sets the stage for their applications to integrable systems, cluster algebras, total positivity, and toric degenerations of Poisson varieties, some of which are discussed in the Introduction. |
Persistent Identifier | http://hdl.handle.net/10722/294083 |
ISSN | 2021 Impact Factor: 1.530 2020 SCImago Journal Rankings: 1.757 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Elek, B | - |
dc.contributor.author | Lu, JH | - |
dc.date.accessioned | 2020-11-23T08:26:05Z | - |
dc.date.available | 2020-11-23T08:26:05Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | International Mathematics Research Notices, 2021, v. 2021 n. 14, p. 10745-10797 | - |
dc.identifier.issn | 1073-7928 | - |
dc.identifier.uri | http://hdl.handle.net/10722/294083 | - |
dc.description.abstract | We show that associated with any n-dimensional Bott–Samelson variety of a complex semi-simple Lie group G, one has 2n Poisson brackets on the polynomial algebra A=C[z1,…,zn], each an iterated Poisson Ore extension and one of them a symmetric Poisson Cauchon–Goodearl–Letzter (CGL) extension in the sense of Goodearl–Yakimov. We express the Poisson brackets in terms of root strings and structure constants of the Lie algebra of G. It follows that the coordinate rings of all generalized Bruhat cells have presentations as symmetric Poisson CGL extensions. The paper establishes the foundation on generalized Bruhat cells and sets the stage for their applications to integrable systems, cluster algebras, total positivity, and toric degenerations of Poisson varieties, some of which are discussed in the Introduction. | - |
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 | Post-print: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [International Mathematics Research Notices] following peer review. The definitive publisher-authenticated version [International Mathematics Research Notices, 2021, v. 2021 n. 14, p. 10745-10797] is available online at: [http://dx.doi.org/10.1093/imrn/rnz127]. | - |
dc.title | Bott–samelson Varieties And Poisson Ore Extensions | - |
dc.type | Article | - |
dc.identifier.email | Lu, JH: jhluhku@hku.hk | - |
dc.identifier.authority | Lu, JH=rp00753 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1093/imrn/rnz127 | - |
dc.identifier.scopus | eid_2-s2.0-85115666651 | - |
dc.identifier.hkuros | 319315 | - |
dc.identifier.volume | 2021 | - |
dc.identifier.issue | 14 | - |
dc.identifier.spage | 10745 | - |
dc.identifier.epage | 10797 | - |
dc.identifier.isi | WOS:000731071200010 | - |
dc.publisher.place | United Kingdom | - |