In the present article we discuss the classification of quantum groups whose quasiclassical limit is a given simple complex Lie algebra g. This problem reduces to the classification of all Lie bialgebra structures on g(K), where K = C((hbar)). The associated classical double is of the form g(K)⊗K A, where A is one of the following: K[ε], where ε2 =0, K ⊕ K or K[j], where j2 = hbar. The first case relates 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 from the Belavin-Drinfeld list [1]. We prove a one-to-one correspondence between gauge equivalence classes of Lie bialgebra structures on g(K) and cohomology classes (in case II) a...
A Lie bialgebra is a vector space endowed simultaneously with the structure of a Lie algebra and the...
Let G be a complex non-exceptional simple algebraic group and g its Lie algebra. With every point x ...
We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint...
In the present article we discuss the classification of quantum groups whose quasiclassical limit is...
In the present article we discuss the classification of quantum groups whose quasi-classical limit i...
In the present article we discuss the classification of quantum groups whose quasi-classical limit i...
In this paper we continue to study Belavin-Drinfeld cohomology introduced in Kadets et al., Commun. ...
In this paper we continue to study Belavin-Drinfeld cohomology introduced in Kadets et al., Commun. ...
Given an arbitrary field of characteristic 0, we study Lie bialgebra structures on sl(n, ), based on...
Given an arbitrary field of characteristic 0, we study Lie bialgebra structures on sl(n, ), based on...
Given an arbitrary field F of characteristic 0, we study Lie bialgebra structures on sl(n,F), based ...
Given an arbitrary field F of characteristic 0, we study Lie bialgebra structures on sl(n,F), based ...
The first example of a quantum group was introduced by P. Kulish and N. Reshetikhin. In the paper Ku...
This book provides a thorough introduction to the theory of complex semisimple quantum groups, that ...
The first example of a quantum group was introduced by P.\ua0Kulish and N.\ua0Reshetikhin. In the pa...
A Lie bialgebra is a vector space endowed simultaneously with the structure of a Lie algebra and the...
Let G be a complex non-exceptional simple algebraic group and g its Lie algebra. With every point x ...
We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint...
In the present article we discuss the classification of quantum groups whose quasiclassical limit is...
In the present article we discuss the classification of quantum groups whose quasi-classical limit i...
In the present article we discuss the classification of quantum groups whose quasi-classical limit i...
In this paper we continue to study Belavin-Drinfeld cohomology introduced in Kadets et al., Commun. ...
In this paper we continue to study Belavin-Drinfeld cohomology introduced in Kadets et al., Commun. ...
Given an arbitrary field of characteristic 0, we study Lie bialgebra structures on sl(n, ), based on...
Given an arbitrary field of characteristic 0, we study Lie bialgebra structures on sl(n, ), based on...
Given an arbitrary field F of characteristic 0, we study Lie bialgebra structures on sl(n,F), based ...
Given an arbitrary field F of characteristic 0, we study Lie bialgebra structures on sl(n,F), based ...
The first example of a quantum group was introduced by P. Kulish and N. Reshetikhin. In the paper Ku...
This book provides a thorough introduction to the theory of complex semisimple quantum groups, that ...
The first example of a quantum group was introduced by P.\ua0Kulish and N.\ua0Reshetikhin. In the pa...
A Lie bialgebra is a vector space endowed simultaneously with the structure of a Lie algebra and the...
Let G be a complex non-exceptional simple algebraic group and g its Lie algebra. With every point x ...
We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint...