Related papers: Quantization of color Lie bialgebras
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 modify the quantization of Etingof and Kazhdan so that it can be used to quantize quasi-Lie bialgebras.
For every semi-simple Lie algebra one can construct the Drinfeld-Jimbo algebra U. This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U, Drinfeld used the KZ-equations to…
In the paper "On some unsolved problems in quantum group theory", V.Drinfeld formulated the problem of the existence of a universal quantization for Lie bialgebras. When the paper "Tensor structures arising from affine Lie algebras, III",…
We develop the cohomology theory of color Lie superalgebras due to Scheunert--Zhang in a framework of nonhomogeneous quadratic Koszul algebras. In this approach, the Chevalley--Eilenberg complex of a color Lie algebra becomes a standard…
The aim of this article is to give a quantization of some coisotropic subalgebras in complex semisimple Lie bialgebras. The coisotropic subalgebras that will be quantized are those given by Zambon in his paper "`A Construction for…
For a given Lie superalgebra, two ways of constructing color superalgebras are presented. One of them is based on the color superalgebraic nature of the Clifford algebras. The method is applicable to any Lie superalgebras and results in…
Let k be a field of characteristic not two or three, let $\mathfrak{g}$ be a finite-dimensional colour Lie algebra and let V be a finite-dimensional representation of $\mathfrak{g}$. In this article we give various ways of constructing a…
The notion of color algebras is generalized to the class of F-ary algebras, and corresponding decoloration theorems are established. This is used to give a construction of colored structures by means of tensor products with Clifford-like…
The purpose of this paper is to generalize some results on $n$-Lie algebras and $n$-Hom-Lie algebras to $n$-Hom-Lie color algebras. Then we introduce and give some constructions of $n$-Hom-Lie color algebras.
The representations of various color Lie superalgebras by Hilbert series are the main topic of this work. The Color Lie superalgebras appear in various branches of mathematics (e.g., topology, algebraic groups, etc.). They are generalized…
We describe a type of Lie color algebra, which we call generic, whose universal enveloping algebra is a domain with finite global dimension. Moreover, it is an iterated Ore extension. We provide an application and show Grobner basis methods…
The purpose of this paper is to study quadratic color Hom-Lie algebras. We present some constructions of quadratic color Hom-Lie algebras which we use to provide several examples. We describe $T^\ast$-extensions and central extensions of…
Drinfeld Yangian of a queer Lie superalgebra is defined as the quantization of a Lie bisuperelgebra of twisted polynomial currents. An analogue of the new system of generators of Drinfeld is being constructed. It is proved for the partial…
The notions of Lie color 2-algebras and 2-term color L-infty-algebras over a group-graded vector space are introduced and studied. It is proved that the category of Lie color 2-algebras and the category of 2-term color L1-algebras are…
A perturbative quantization procedure for Lie bialgebras is introduced and used to classify all three dimensional complex quantum algebras compatible with a given coproduct. The role of elements of the quantum universal enveloping algebra…
The purpose of this paper is to generalize some results on ternary Leibniz algebras to the case of ternary Leibniz color algebras. In particular, we study color Lie triple systems. In order to produce examples of ternary Leibniz color…
We adapt methods from the theory of complex semisimple Lie algebras to develop a root theory for a class of simple $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded (color) Lie algebras, which we call basic. As an application, assuming that the…
The class of generalized Lie-type color algebras contains the ones of generalized Lie-type algebras, of $n$-Lie algebras and superalgebras, commutative Leibniz $n$-ary algebras and superalgebras, among others. We focus on the class of…
The aim of this paper is introduce and give some constructions results and examples of n-BiHom-Lie color algebras. Next, we introduce the definition of BiHom-modules over n- BiHom-Lie color algebras and we provide some properties. Moreover…