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dc.contributor.author
Andruskiewitsch, Nicolas
dc.contributor.author
Angiono, Iván Ezequiel
dc.contributor.author
Istvan, Romina Mariel
dc.date.available
2022-10-17T12:34:21Z
dc.date.issued
2021-08-11
dc.identifier.citation
Andruskiewitsch, Nicolas; Angiono, Iván Ezequiel; Istvan, Romina Mariel; On finite GK-dimensional Nichols algebra over abelian groups; American Mathematical Society; Memoirs Of The American Mathematical Society (ams); 271; 1329; 11-8-2021; 1-130
dc.identifier.isbn
978-1-4704-4830-1
dc.identifier.issn
0065-9266
dc.identifier.uri
http://hdl.handle.net/11336/173428
dc.description.abstract
We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GKdim for short, through the study of Nichols algebras over abelian groups. We deal first with braided vector spaces over Z with the generator acting as a single Jordan block and show that the corresponding Nichols algebra has finite GKdim if and only if the size of the block is 2 and the eigenvalue is ±1; when this is 1, we recover the quantum Jordan plane. We consider next a class of braided vector spaces that are direct sums of blocks and points that contains those of diagonal type.We conjecture that a Nichols algebra of diagonal type has finite GKdim if and only if the corresponding generalized root system is finite. Assuming the validity of this conjecture, we classify all braided vector spaces in the mentioned class whose Nichols algebra has finite GKdim. Consequently we present several new examples of Nichols algebras with finite GKdim, including two not in the class alluded to above. We determine which among these Nichols algebras are domains.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Mathematical Society
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Hopf algebras
dc.subject
Nichols algebras
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Gelfand-Kirillov dimension
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
On finite GK-dimensional Nichols algebra over abelian 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
2022-09-19T16:06:25Z
dc.journal.volume
271
dc.journal.number
1329
dc.journal.pagination
1-130
dc.journal.pais
Estados Unidos
dc.journal.ciudad
Providence
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: Istvan, Romina Mariel. University Of Marburg; Alemania
dc.journal.title
Memoirs Of The American Mathematical Society (ams)
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1090/memo/1329
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/books/memo/1329/
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