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dc.contributor.authorVicedo, Benoit
dc.contributor.authorYoung, Charles A. S.
dc.date.accessioned2017-01-12T13:42:48Z
dc.date.available2017-01-12T13:42:48Z
dc.date.issued2016-03-30
dc.identifier.citationVicedo , B & Young , C A S 2016 , ' Vertex Lie algebras and cyclotomic coinvariants ' , Communications in Contemporary Mathematics , vol. 19 , no. 2 . https://doi.org/10.1142/S0219199716500152
dc.identifier.issn0219-1997
dc.identifier.otherArXiv: http://arxiv.org/abs/1410.7664v1
dc.identifier.otherORCID: /0000-0002-7490-1122/work/55503515
dc.identifier.urihttp://hdl.handle.net/2299/17503
dc.descriptionElectronic version of an article published as Benoît Vicedo and Charles Young, Commun. Contemp. Math. 0, 1650015 (2016) [62 pages] DOI: http://dx.doi.org/10.1142/S0219199716500152 Vertex Lie algebras and cyclotomic coinvariants.
dc.description.abstractGiven a vertex Lie algebra $\mathscr L$ equipped with an action by automorphisms of a cyclic group $\Gamma$, we define spaces of cyclotomic coinvariants over the Riemann sphere. These are quotients of tensor products of smooth modules over `local' Lie algebras $\mathsf L(\mathscr L)_{z_i}$ assigned to marked points $z_i$, by the action of a `global' Lie algebra ${\mathsf L}^{\Gamma}_{\{z_i \}}(\mathscr L)$ of $\Gamma$-equivariant functions. On the other hand, the universal enveloping vertex algebra $\mathbb V (\mathscr L)$ of $\mathscr L$ is itself a vertex Lie algebra with an induced action of $\Gamma$. This gives `big' analogs of the Lie algebras above. From these we construct the space of `big' cyclotomic coinvariants, i.e. coinvariants with respect to ${\mathsf L}^{\Gamma}_{\{z_i \}}(\mathbb V(\mathscr L))$. We prove that these two definitions of cyclotomic coinvariants in fact coincide, provided the origin is included as a marked point. As a corollary we prove a result on the functoriality of cyclotomic coinvariants which we require for the solution of cyclotomic Gaudin models in arXiv:1409.6937. At the origin, which is fixed by $\Gamma$, one must assign a module over the stable subalgebra $\mathsf L(\mathscr L)^{\Gamma}$ of $\mathsf L(\mathscr L)$. This module becomes a $\mathbb V(\mathscr L)$-quasi-module in the sense of Li. As a bi-product we obtain an iterate formula for such quasi-modules.en
dc.format.extent62
dc.format.extent759403
dc.language.isoeng
dc.relation.ispartofCommunications in Contemporary Mathematics
dc.subjectmath.QA
dc.subjectvertex algebras
dc.subjectvertex Lie algebras
dc.subjectcyclotomic coinvariants
dc.subjectinfinite dimensional Lie algebras
dc.titleVertex Lie algebras and cyclotomic coinvariantsen
dc.contributor.institutionSchool of Physics, Astronomy and Mathematics
dc.description.statusPeer reviewed
dc.date.embargoedUntil2017-03-30
rioxxterms.versionofrecord10.1142/S0219199716500152
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue


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