Related papers: Drinfeld-Jimbo quantum Lie algebra
We describe a quantum Lie algebra based on the Cremmer-Gervais R-matrix. The algebra arises upon a restriction of an infinite-dimensional quantum Lie algebra.
Quantum Lie algebras $\qlie{g}$ are non-associative algebras which are embedded into the quantized enveloping algebras $U_q(g)$ of Drinfeld and Jimbo in the same way as ordinary Lie algebras are embedded into their enveloping algebras. The…
We show explicitly a generalised Lie algebra embedded in the positive and negative parts of the Drinfeld-Jimbo quantum groups of type A_n. Such a generalised Lie algebra satisfy axioms closely related to the ones found by S.L. Woronowicz.…
In this paper we continue to study Belavin-Drinfeld cohomology introduced in arXiv:1303.4046 [math.QA] and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra. Here we compute…
Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided…
In this paper we use the Etingof-Kazhdan quantization of Lie bi-superalgebras to investigate some interesting questions related to Drinfeld-Jimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that…
We describe (braided-)commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over…
Let $G$ be a simple complex classical group and $\g$ its Lie algebra. Let $\U_\hbar(\g)$ be the Drinfeld-Jimbo quantization of the universal enveloping algebra $\U(\g)$. We construct an explicit $\U_\hbar(\g)$-equivariant quantization of…
Multiparametric quantum deformations of $gl(2)$ are studied through a complete classification of $gl(2)$ Lie bialgebra structures. From them, the non-relativistic limit leading to harmonic oscillator Lie bialgebras is implemented by means…
It is shown that the quantised enveloping algebra of sl(n) contains a quantum Lie algebra, defined by means of axioms similar to Woronowicz's., This gives rise to Lie algebra-like generators and relations for the locally finite part of the…
The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.
We summarise the classification of kinematical Lie algebras in arbitrary dimension and indicate which of the kinematical Lie algebras admit an invariant inner product.
The present article is a continuation of QA/1303.4046, where we discussed the classification of quantum groups with quasi-classical limit $\mathfrak{g}$ and introduced a theory of Belavin-Drinfeld cohomology associated to any…
In this paper, we focus on $(n+3)$-dimensional metric $n$-Lie algebras. To begin with, we give some properties on $(n+3)$-dimensional $n$-Lie algebras. Then based on the properties, we obtain the classification of $(n+3)$-dimensional metric…
We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms faithfully flat cohomology over an arbitrary ring…
We construct the first examples of purely continuous, $q$-deformed Lie type locally compact quantum groups in higher rank. They arise from Drinfeld-Jimbo quantization, at unimodular deformation parameter, of the totally positive part of…
In the present article we discuss the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra $\mathfrak{g}$. This problem reduces to the classification of all Lie bialgebra structures on…
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in $h$. They are derived from the quantized enveloping algebras $\uqg$. The quantum Lie bracket satisfies a generalization of antisymmetry.…
In our preceding research, we introduced the Drinfeld presentation of the quantum affine superalgebra associated to the orthosymplectic Lie superalgebra $\mathfrak{osp}(2m+1|2n)$ for $m>0$. We provided the isomorphism between its…
Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, \mu, \gamma ,\phi ?), correspond one Lie algebra structure on D = G\oplus G*, called…