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dc.contributor.author
Karolinsky, Eugene
dc.contributor.author
Pianzola, Arturo
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dc.contributor.author
Stolin, Alexander
dc.date.available
2022-06-10T12:54:45Z
dc.date.issued
2019-11
dc.identifier.citation
Karolinsky, Eugene; Pianzola, Arturo; Stolin, Alexander; Classification of Quantum Groups via Galois Cohomology; Springer; Communications In Mathematical Physics; 377; 11-2019; 1099-1129
dc.identifier.issn
0010-3616
dc.identifier.uri
http://hdl.handle.net/11336/159460
dc.description.abstract
The first example of a quantum group was introduced by P. Kulish and N. Reshetikhin. In the paper Kulish et al. (J Soviet Math 23:2435–2441, 1983), they found a new algebra which was later called Uq(sl(2)). Their example was developed independently by V. Drinfeld and M. Jimbo, which resulted in the general notion of quantum group. Later, a complimentary approach to quantum groups was developed by L. Faddeev, N. Reshetikhin, and L. Takhtajan in Faddeev et al. (Leningr Math J 1:193–225, 1990). Recently, the so-called Belavin–Drinfeld cohomology (twisted and non-twisted) have been introduced in the literature to study and classify certain families of quantum groups and Lie bialgebras. Later, the last two authors interpreted non-twisted Belavin–Drinfeld cohomology in terms of non-abelian Galois cohomology H1(F,H) for a suitable algebraic F-group H. Here F is an arbitrary field of zero characteristic. The non-twisted case is thus fully understood in terms of Galois cohomology. The twisted case has only been studied using Galois cohomology for the so-called (“standard”) Drinfeld–Jimbo structure. The aim of the present paper is to extend these results to all twisted Belavin–Drinfeld cohomology and thus, to present classification of quantum groups in terms of Galois cohomology and the so-called orders. Low dimensional cases sl(2) and sl(3) are considered in more details using a theory of cubic rings developed by B. N. Delone and D. K. Faddeev in Delone and Faddeev (The theory of irrationalities of the third degree. Translations of mathematical monographs, vol 10. AMS, Providence, 1964). Our results show that there exist yet unknown quantum groups for Lie algebras of the types An,D2n+1,E6, not mentioned in Etingof et al. (J Am Math Soc 13:595–609, 2000).
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
QUANTUM GROUPS
dc.subject
GALOIS COHOMOLOGY
dc.subject
BELAVIN-DRINFELD
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
Classification of Quantum Groups via Galois Cohomology
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-06-09T13:31:14Z
dc.journal.volume
377
dc.journal.pagination
1099-1129
dc.journal.pais
Alemania
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dc.journal.ciudad
Berlín
dc.description.fil
Fil: Karolinsky, Eugene. Kharkiv National University. Department of Pure Mathematics; Ucrania
dc.description.fil
Fil: Pianzola, Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. University of Alberta; Canadá. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina
dc.description.fil
Fil: Stolin, Alexander. University Goteborg; Suecia
dc.journal.title
Communications In Mathematical Physics
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00220-019-03597-z
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00220-019-03597-z
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