Degree cones and monomial bases of lie algebras and quantum groups

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dc.identifier.uri Backhaus, Teodor Fang, Xin Fourier, Ghislain 2017-11-17T08:34:56Z 2018-03-20T23:05:15Z 2017
dc.identifier.citation Backhaus, T.; Fang, X.; Fourier, G.: Degree cones and monomial bases of lie algebras and quantum groups. In: Glasgow Mathematical Journal 59 (2017), Nr. 3, S. 595-621. DOI:
dc.description.abstract We provide ℕ-filtrations on the negative part Uq ((Formula presented.) −) of the quantum group associated to a finite-dimensional simple Lie algebra (Formula presented.), such that the associated graded algebra is a skew-polynomial algebra on (Formula presented.) −. The filtration is obtained by assigning degrees to Lusztig's quantum PBW root vectors. The possible degrees can be described as lattice points in certain polyhedral cones. In the classical limit, such a degree induces an ℕ-filtration on any finite-dimensional simple (Formula presented.)-module. We prove for type An, Cn, B3, D4 and G2 that a degree can be chosen such that the associated graded modules are defined by monomial ideals, and conjecture that this is true for any (Formula presented.). Copyright © Glasgow Mathematical Journal Trust 2017 eng
dc.language.iso eng
dc.publisher Cambridge : Cambridge University Press
dc.relation.ispartofseries Glasgow Mathematical Journal 59 (2017), Nr. 3
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
dc.subject degree cones eng
dc.subject monomial bases eng
dc.subject lie algebras eng
dc.subject quantum groups eng
dc.subject.ddc 510 | Mathematik ger
dc.title Degree cones and monomial bases of lie algebras and quantum groups
dc.type article
dc.type Text
dc.relation.issn 0017-0895
dc.bibliographicCitation.issue 3
dc.bibliographicCitation.volume 59
dc.bibliographicCitation.firstPage 595
dc.bibliographicCitation.lastPage 621
dc.description.version publishedVersion
tib.accessRights frei zug�nglich

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