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dc.contributor.author
Andruskiewitsch, Nicolas
dc.contributor.author
Angiono, Iván Ezequiel
dc.date.available
2018-09-17T17:52:19Z
dc.date.issued
2017-12
dc.identifier.citation
Andruskiewitsch, Nicolas; Angiono, Iván Ezequiel; On finite dimensional Nichols algebras of diagonal type; SpringerOpen; Bulletin of Mathematical Sciences; 7; 3; 12-2017; 353-573
dc.identifier.issn
1664-3615
dc.identifier.uri
http://hdl.handle.net/11336/59909
dc.description.abstract
This is a survey on Nichols algebras of diagonal type with finite dimension, or more generally with arithmetic root system. The knowledge of these algebras is the cornerstone of the classification program of pointed Hopf algebras with finite dimension, or finite Gelfand–Kirillov dimension; and their structure should be indispensable for the understanding of the representation theory, the computation of the various cohomologies, and many other aspects of finite dimensional pointed Hopf algebras. These Nichols algebras were classified in Heckenberger (Adv Math 220:59–124, 2009) as a notable application of the notions of Weyl groupoid and generalized root system (Heckenberger in Invent Math 164:175–188, 2006; Heckenberger and Yamane in Math Z 259:255–276, 2008). In the first part of this monograph, we give an overview of the theory of Nichols algebras of diagonal type. This includes a discussion of the notion of generalized root system and its appearance in the contexts of Nichols algebras of diagonal type and (modular) Lie superalgebras. In the second and third part, we describe for each Nichols algebra in the list of Heckenberger (2009) the following basic information: the generalized root system; its label in terms of Lie theory; the defining relations found in Angiono (J Eur Math Soc 17:2643–2671, 2015; J Reine Angew Math 683:189–251, 2013); the PBW-basis; the dimension or the Gelfand–Kirillov dimension; the associated Lie algebra as in Andruskiewitsch et al. (Bull Belg Math Soc Simon Stevin 24(1):15–34, 2017). Indeed the second part deals with Nichols algebras related to Lie algebras and superalgebras in arbitrary characteristic, while the third contains the information on Nichols algebras related to Lie algebras and superalgebras only in small characteristic, and the few examples yet unidentified in terms of Lie theory.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
SpringerOpen
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Modular Lie Algebras
dc.subject
Nichols Algebras
dc.subject
Quantum Groups
dc.subject
Weyl Groupoid
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
On finite dimensional Nichols algebras of diagonal type
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-09-14T19:04:58Z
dc.identifier.eissn
1664-3607
dc.journal.volume
7
dc.journal.number
3
dc.journal.pagination
353-573
dc.journal.pais
Alemania
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.journal.title
Bulletin of Mathematical Sciences
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs13373-017-0113-x
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1007/s13373-017-0113-x
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