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Göteborgs universitets publikationer

Classification of Quantum Groups and Belavin-Drinfeld Cohomologies

Författare och institution:
B. Kadets (-); E. Karolinsky (-); Iulia Pop (Institutionen för matematiska vetenskaper, Chalmers/GU); Alexander Stolin (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Communications in Mathematical Physics, 344 ( 1 )
ISSN:
0010-3616
E-ISSN:
1432-0916
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2016
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
In the present article we discuss the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra g. This problem is reduced to the classification of all Lie bialgebra structures on g(K) , where K= C((ħ)). The associated classical double is of the form g(K) ⊗ KA, where A is one of the following: K[ ε] , where ε2= 0 , K⊕ K or K[ j] , where j2= ħ. The first case is related to quasi-Frobenius Lie algebras. In the second and third cases we introduce a theory of Belavin–Drinfeld cohomology associated to any non-skewsymmetric r-matrix on the Belavin–Drinfeld list (Belavin and Drinfeld in Soviet Sci Rev Sect C: Math Phys Rev 4:93–165, 1984). We prove a one-to-one correspondence between gauge equivalence classes of Lie bialgebra structures on g(K) and cohomology classes (in case II) and twisted cohomology classes (in case III) associated to any non-skewsymmetric r-matrix.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Postens nummer:
241819
Posten skapad:
2016-09-15 08:31

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