dc.contributor.author | NeguΘ, Andrei | |
dc.date.accessioned | 2024-07-11T20:41:13Z | |
dc.date.available | 2024-07-11T20:41:13Z | |
dc.date.issued | 2024-06-25 | |
dc.identifier.issn | 1022-1824 | |
dc.identifier.issn | 1420-9020 | |
dc.identifier.uri | https://hdl.handle.net/1721.1/155661 | |
dc.description.abstract | As a quantum affinization, the quantum toroidal algebra 𝑈𝑞,𝑞β―β―β―(𝔤𝔩¨𝑛)
is defined in terms of its “left” and “right” halves, which both admit shuffle algebra presentations (Enriquez in Transform Groups 5(2):111–120, 2000; Feigin and Odesskii in Am Math Soc Transl Ser 2:185, 1998). In the present paper, we take an orthogonal viewpoint, and give shuffle algebra presentations for the “top” and “bottom” halves instead, starting from the evaluation representation 𝑈𝑞(𝔤𝔩Λ𝑛)β·β𝑛(𝑧)
and its usual R-matrix 𝑅(𝑧)∈End(β𝑛⊗β𝑛)(𝑧)
(see Faddeev et al. in Leningrad Math J 1:193–226, 1990). An upshot of this construction is a new topological coproduct on 𝑈𝑞,𝑞β―β―β―(𝔤𝔩¨𝑛)
which extends the Drinfeld–Jimbo coproduct on the horizontal subalgebra 𝑈𝑞(𝔤𝔩Λ𝑛)⊂𝑈𝑞,𝑞β―β―β―(𝔤𝔩¨𝑛). | en_US |
dc.publisher | Springer Science and Business Media LLC | en_US |
dc.relation.isversionof | 10.1007/s00029-024-00941-7 | en_US |
dc.rights | Creative Commons Attribution | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_US |
dc.source | Springer International Publishing | en_US |
dc.title | A tale of two shuffle algebras | en_US |
dc.type | Article | en_US |
dc.identifier.citation | NeguΘ, A. A tale of two shuffle algebras. Sel. Math. New Ser. 30, 62 (2024). | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
dc.identifier.mitlicense | PUBLISHER_CC | |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2024-06-30T03:10:47Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | The Author(s) | |
dspace.embargo.terms | N | |
dspace.date.submission | 2024-06-30T03:10:47Z | |
mit.journal.volume | 30 | en_US |
mit.journal.issue | 4 | en_US |
mit.license | OPEN_ACCESS_POLICY | |
mit.metadata.status | Authority Work and Publication Information Needed | en_US |