In this paper we continue to study Belavin–Drinfeld cohomology introduced in Kadets et al., Commun. Math. Phys. 344(1), 1-24 (2016) and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra 𝔤. Here we compute Belavin–Drinfeld cohomology for all non-skewsymmetric r-matrices on the Belavin–Drinfeld list for simple Lie algebras of type B, C, and D.
REFERENCES
1.
Belavin
, A.
and Drinfeld
, V.
, “Triangle equations and simple Lie algebras
,” Sov. Sci. Rev., Sect. C: Math. Phys. Rev.
4
, 93
–165
(1984
).2.
Drinfeld
, V.
, “Hopf algebras and the quantum Yang-Baxter equation
,” Dokl. Akad. Nauk SSSR
283
(5
), 1060
–1064
(1985
).3.
Etingof
, P.
and Kazhdan
, D.
, “Quantization of Lie bialgebras I
,” Sel. Math.
2
, 1
–41
(1996
).4.
Etingof
, P.
and Kazhdan
, D.
, “Quantization of Lie bialgebras II
,” Sel. Math.
4
, 213
–232
(1998
).5.
Etingof
, P.
and Schiffmann
, O.
, Lectures on Quantum Groups
(International Press
, Cambridge
, 1988
).6.
Etingof
, P.
, Schedler
, T.
, and Schiffmann
, O.
, “Explicit quantization of dynamical r-matrices for finite dimensional semisimple Lie algebras
,” J. Am. Math. Soc.
13
(3
), 595
–609
(2000
).7.
Jimbo
, M.
, “A q-difference analogue of U𝔤 and the Yang-Baxter equation
,” Lett. Math. Phys.
10
, 63
–69
(1985
).8.
Kadets
, B.
, Karolinsky
, E.
, Pop
, I.
, and Stolin
, A.
, “Classification of quantum groups and Belavin–Drinfeld cohomologies
,” Commun. Math. Phys.
344
(1
), 1
–24
(2016
).9.
Kulish
, P. P.
and Reshetikhin
, N. Yu.
, “Quantum linear problem for the sine-Gordon equation and higher representations
,” J. Sov. Math.
23
, 2435
–2441
(1983
).10.
Stolin
, A.
, “Some remarks on Lie bialgebra structures on simple complex Lie algebras
,” Commun. Algebra
27
, 4289
–4302
(1999
).11.
Stolin
, A.
and Pop
, I.
, “Classification of quantum groups and Lie bialgebra structures on sl(n, F). Relations with Brauer group
,” Adv. Math.
293
, 324
–342
(2016
).© 2016 Author(s).
2016
Author(s)
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