dc.contributor.author | Vicedo, Benoit | |
dc.contributor.author | Young, Charles A. S. | |
dc.date.accessioned | 2017-01-12T13:42:48Z | |
dc.date.available | 2017-01-12T13:42:48Z | |
dc.date.issued | 2016-03-30 | |
dc.identifier.citation | Vicedo , 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.issn | 0219-1997 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1410.7664v1 | |
dc.identifier.other | ORCID: /0000-0002-7490-1122/work/55503515 | |
dc.identifier.uri | http://hdl.handle.net/2299/17503 | |
dc.description | Electronic 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.abstract | Given 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.extent | 62 | |
dc.format.extent | 759403 | |
dc.language.iso | eng | |
dc.relation.ispartof | Communications in Contemporary Mathematics | |
dc.subject | math.QA | |
dc.subject | vertex algebras | |
dc.subject | vertex Lie algebras | |
dc.subject | cyclotomic coinvariants | |
dc.subject | infinite dimensional Lie algebras | |
dc.title | Vertex Lie algebras and cyclotomic coinvariants | en |
dc.contributor.institution | School of Physics, Astronomy and Mathematics | |
dc.description.status | Peer reviewed | |
dc.date.embargoedUntil | 2017-03-30 | |
rioxxterms.versionofrecord | 10.1142/S0219199716500152 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |