Show simple item record

dc.contributor.authorNeguΘ›, Andrei
dc.date.accessioned2024-07-11T20:41:13Z
dc.date.available2024-07-11T20:41:13Z
dc.date.issued2024-06-25
dc.identifier.issn1022-1824
dc.identifier.issn1420-9020
dc.identifier.urihttps://hdl.handle.net/1721.1/155661
dc.description.abstractAs a quantum affinization, the quantum toroidal algebra 𝑈𝑞,𝑞⎯⎯⎯(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(𝔤𝔩Λ™𝑛)β†·β„‚𝑛(𝑧) and its usual R-matrix 𝑅(𝑧)∈End(β„‚𝑛⊗β„‚𝑛)(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,𝑞⎯⎯⎯(𝔤𝔩¨𝑛) which extends the Drinfeld–Jimbo coproduct on the horizontal subalgebra 𝑈𝑞(𝔤𝔩Λ™𝑛)⊂𝑈𝑞,𝑞⎯⎯⎯(𝔤𝔩¨𝑛).en_US
dc.publisherSpringer Science and Business Media LLCen_US
dc.relation.isversionof10.1007/s00029-024-00941-7en_US
dc.rightsCreative Commons Attributionen_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.sourceSpringer International Publishingen_US
dc.titleA tale of two shuffle algebrasen_US
dc.typeArticleen_US
dc.identifier.citationNeguΘ›, A. A tale of two shuffle algebras. Sel. Math. New Ser. 30, 62 (2024).en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.identifier.mitlicensePUBLISHER_CC
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2024-06-30T03:10:47Z
dc.language.rfc3066en
dc.rights.holderThe Author(s)
dspace.embargo.termsN
dspace.date.submission2024-06-30T03:10:47Z
mit.journal.volume30en_US
mit.journal.issue4en_US
mit.licenseOPEN_ACCESS_POLICY
mit.metadata.statusAuthority Work and Publication Information Neededen_US
ο»Ώ

Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record