Publication
Extended graphical calculus for categorified quantum sl(2)
| dc.contributor.author | Khovanov, Mikhail | |
| dc.contributor.author | Lauda, Aaron | |
| dc.contributor.author | Mackaay, Marco | |
| dc.contributor.author | Stošić, Marko | |
| dc.date.accessioned | 2021-02-19T13:21:44Z | |
| dc.date.available | 2021-02-19T13:21:44Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in the paper arXiv:0803.3652 by the second author. Here we enhance the graphical calculus introduced and developed in that paper to include two-morphisms between divided powers one-morphisms and their compositions. We obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms; the latter are in a bijection with the Lusztig canonical basis elements. These formulas have integral coefficients and imply that one of the main results of Lauda’s paper—identification of the Grothendieck ring of his 2-category with the idempotented quantum sl(2)—also holds when the 2-category is defined over the ring of integers rather than over a field. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.doi | 10.1090/S0065-9266-2012-00665-4 | pt_PT |
| dc.identifier.uri | http://hdl.handle.net/10400.1/15130 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | American Mathematical Societ | pt_PT |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | pt_PT |
| dc.title | Extended graphical calculus for categorified quantum sl(2) | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 0 | pt_PT |
| oaire.citation.issue | 1029 | pt_PT |
| oaire.citation.startPage | 0 | pt_PT |
| oaire.citation.title | Memoirs of the American Mathematical Society | pt_PT |
| oaire.citation.volume | 219 | pt_PT |
| person.familyName | MACKAAIJ | |
| person.givenName | MARCO | |
| person.identifier.ciencia-id | F810-F5CB-9F35 | |
| person.identifier.orcid | 0000-0001-9807-6991 | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
| relation.isAuthorOfPublication | 62310e63-1319-4bf3-87c8-1f6790d9f190 | |
| relation.isAuthorOfPublication.latestForDiscovery | 62310e63-1319-4bf3-87c8-1f6790d9f190 |