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dc.contributor.author
Guo, Hongyan
dc.contributor.author
Kuttler, Jochen
dc.contributor.author
Pianzola, Arturo
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dc.date.available
2024-08-29T11:05:57Z
dc.date.issued
2023-06
dc.identifier.citation
Guo, Hongyan; Kuttler, Jochen; Pianzola, Arturo; Descent study of the Lie algebra of derivations of certain infinite-dimensional Lie algebras; Springer; Manuscripta Mathematica; 173; 3-4; 6-2023; 1195-1215
dc.identifier.issn
0025-2611
dc.identifier.uri
http://hdl.handle.net/11336/243282
dc.description.abstract
Letgbeafinite-dimensionalperfectLiealgebraoverafieldkofcharacteristic0. In infinite-dimensional Lie theory we encounter Lie algebras of the form g⊗k R, where R is a k-ring (usually a Laurent polynomial ring in finitely many variables over k), and étale twisted forms L of g⊗k R. Thus L is an R-Lie algebra that becomes isomorphic to the S-Lie algebra g ⊗k S after some étale cover base ring extension S/R. The interesting infinite-dimensional Lie algebras are “built” out of L by adding a centre Z and a Lie algebra of derivations D (the affine Kac-Moody Lie algebras are the simplest examples). D, which determines Z, is a Lie subalgebra of Derk(L) of L. The understanding of this last Lie algebra is crucial. While the R-Lie algebra L can be given by étale descent, the same cannot be openly said about Derk(L) since it is not an R-Lie algebra. In the present paper we give such a descent presentation within the more general framework of relative R/k-sheaves of Lie algebras that we believe is of independent interest.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
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dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Central extensions
dc.subject
Etale descent
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Descent study of the Lie algebra of derivations of certain infinite-dimensional Lie algebras
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-08-28T09:56:21Z
dc.journal.volume
173
dc.journal.number
3-4
dc.journal.pagination
1195-1215
dc.journal.pais
Alemania
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dc.journal.ciudad
Berlin
dc.description.fil
Fil: Guo, Hongyan. Central China Normal University; China
dc.description.fil
Fil: Kuttler, Jochen. University of Alberta; Canadá
dc.description.fil
Fil: Pianzola, Arturo. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. University of Alberta; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.journal.title
Manuscripta Mathematica
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s00229-023-01483-6
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00229-023-01483-6
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