Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 오세진 | * |
dc.date.accessioned | 2018-11-21T16:30:50Z | - |
dc.date.available | 2018-11-21T16:30:50Z | - |
dc.date.issued | 2018 | * |
dc.identifier.issn | 0894-0347 | * |
dc.identifier.other | OAK-22025 | * |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/246876 | - |
dc.description.abstract | We prove that the quantum cluster algebra structure of a unipotent quantum coordinate ring Aq(n(w)), associated with a symmetric Kac-Moody algebra and its Weyl group element w, admits a monoidal categorification via the representations of symmetric Khovanov-Lauda-Rouquier algebras. In order to achieve this goal, we give a formulation of monoidal categorifications of quantum cluster algebras and provide a criterion for a monoidal category of finite-dimensional graded R-modules to become a monoidal categorification, where R is a symmetric Khovanov-Lauda-Rouquier algebra. Roughly speaking, this criterion asserts that a quantum monoidal seed can be mutated successively in all the directions, once the first-step mutations are possible. Then, we show the existence of a quantum monoidal seed of Aq(n(w)) which admits the first-step mutations in all the directions. As a consequence, we prove the conjecture that any cluster monomial is a member of the upper global basis up to a power of q1/2. In the course of our investigation, we also give a proof of a conjecture of Leclerc on the product of upper global basis elements. © 2017 American Mathematical Society. | * |
dc.description.sponsorship | Korea Creative Content Agency | * |
dc.language | English | * |
dc.publisher | American Mathematical Society | * |
dc.subject | Cluster algebra | * |
dc.subject | Khovanov-Lauda-Rouquier algebra | * |
dc.subject | Monoidal categorification | * |
dc.subject | Quantum affine algebra | * |
dc.subject | Quantum cluster algebra | * |
dc.subject | Unipotent quantum coordinate ring | * |
dc.title | Monoidal categorification of cluster algebras | * |
dc.type | Article | * |
dc.relation.issue | 2 | * |
dc.relation.volume | 31 | * |
dc.relation.index | SCIE | * |
dc.relation.index | SCOPUS | * |
dc.relation.startpage | 349 | * |
dc.relation.lastpage | 426 | * |
dc.relation.journaltitle | Journal of the American Mathematical Society | * |
dc.identifier.doi | 10.1090/JAMS/895 | * |
dc.identifier.wosid | WOS:000424115500003 | * |
dc.identifier.scopusid | 2-s2.0-85044032356 | * |
dc.author.google | Kang S.-J. | * |
dc.author.google | Kashiwara M. | * |
dc.author.google | Kim M. | * |
dc.author.google | Oh S.-J. | * |
dc.contributor.scopusid | 오세진(55636183200) | * |
dc.date.modifydate | 20240222164805 | * |