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dc.contributor.author
Andruskiewitsch, Nicolas
dc.contributor.author
Angiono, Iván Ezequiel
dc.contributor.author
Garcia Iglesias, Agustin
dc.date.available
2018-09-04T22:34:56Z
dc.date.issued
2017-05
dc.identifier.citation
Andruskiewitsch, Nicolas; Angiono, Iván Ezequiel; Garcia Iglesias, Agustin; Liftings of Nichols algebras of diagonal type I. cartan type A; Oxford University Press; International Mathematics Research Notices; 2017; 9; 5-2017; 2793-2884
dc.identifier.issn
1073-7928
dc.identifier.uri
http://hdl.handle.net/11336/58327
dc.description.abstract
After the classification of the finite-dimensional Nichols algebras of diagonal type[17,18], the determination of its defining relations[7,6], and the verification of the generation in degree-s1 conjecture[6], there is still one step missing in the classification of complex finite-dimensional Hopf algebras with abelian group, without restrictions on the order of the latter: The computation of all deformations or liftings. A technique towards solving this question was developed in[5], built on cocycle deformations. In this paper, we elaborate further and present an explicit algorithm to compute liftings. In our main result we classify all liftings of finite-dimensional Nichols algebras of Cartan type A, over a cosemisimple Hopf algebra H. This extends[2], where it was assumed that the parameter is a root of unity of order >3 and that H is a commmutative group algebra. When the parameter is a root of unity of order 2 or 3, new phenomena appear: The quantum Serre relations can be deformed; this allows in turn the power root vectors to be deformed to elements in lower terms of the coradical filtration, but not necessarily in the group algebra. These phenomena are already present in the calculation of the liftings in type A2 at a parameter of order 2 or 3 over an abelian group[11,19], done by a different method using a computer program. As a byproduct of our calculations, we present new infinite families of finite-dimensional pointed Hopf algebras.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Oxford University Press
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Hopf Algebras
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Nichols Algebras
dc.subject
Deformations
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Liftings of Nichols algebras of diagonal type I. cartan type A
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-08-15T13:57:36Z
dc.journal.volume
2017
dc.journal.number
9
dc.journal.pagination
2793-2884
dc.journal.pais
Reino Unido
dc.journal.ciudad
Oxford
dc.description.fil
Fil: Andruskiewitsch, Nicolas. 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.description.fil
Fil: Angiono, Iván Ezequiel. 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.description.fil
Fil: Garcia Iglesias, Agustin. 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
International Mathematics Research Notices
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2017/9/2793/3061030?redirectedFrom=fulltext
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1093/imrn/rnw103
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