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dc.contributor.author
Vay, Cristian Damian
dc.date.available
2018-09-19T17:36:27Z
dc.date.issued
2017-11
dc.identifier.citation
Vay, Cristian Damian; On projective modules over finite quantum groups; Birkhauser Boston Inc; Transformation Groups; 11-2017; 1-21
dc.identifier.issn
1083-4362
dc.identifier.uri
http://hdl.handle.net/11336/60240
dc.description.abstract
Let (Formula presented.) be the Drinfeld double of the bosonization (Formula presented.)(V)(Formula presented.)G of a finite-dimensional Nichols algebra (Formula presented.)(V ) over a finite group G. It is known that the simple (Formula presented.)-modules are parametrized by the simple modules over (Formula presented.)(G), the Drinfeld double of G. This parametrization can be obtained by considering the head L(λ) of the Verma module M(λ) for every simple (Formula presented.)(G)-module λ. In the present work, we show that the projective (Formula presented.)-modules are filtered by Verma modules and the BGG Reciprocity [P(μ): M(λ)] = [M(λ): L(μ)] holds for the projective cover P(μ) of L(μ). We use graded characters to prove the BGG Reciprocity and obtain a graded version of it. As a by-product we show that a Verma module is simple if and only if it is projective. We also describe the tensor product between projective modules.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Birkhauser Boston Inc
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Hopf Algebras
dc.subject
Nichols Algebras
dc.subject
Representation Theory
dc.subject
Highest Weight Category
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
On projective modules over finite quantum groups
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-09-14T19:03:45Z
dc.identifier.eissn
1531-586X
dc.journal.pagination
1-21
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Vay, Cristian Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
dc.journal.title
Transformation Groups
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00031-017-9469-y
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00031-017-9469-y
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