相关论文: Quantum deformations for the diagonal R-matrices
$*$-structures on quantum and braided spaces of the type defined via an R-matrix are studied. These include $q$-Minkowski and $q$-Euclidean spaces as additive braided groups. The duality between the $*$-braided groups of vectors and…
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…
We calculate the first Hochschild cohomology group of quantum matrices, the quantum general linear group and the quantum special linear group in the generic case when the deformation parameter is not a root of unity. As a corollary, we…
The principles of the theory of quantum groups are reviewed from the point of view of the possibility of their use for deformations of symmetries in physical models. The R-matrix approach to the theory of quantum groups is discussed in…
In this article we construct $GL_{h}(3)$ from $GL_{q}(3)$ by a singular map. We show that there exist two singular maps which map $GL_{q}(3)$ to new quantum groups. We also construct their $R$-matrices and will show although the maps are…
An explicit construction of the braided dual of quantum $E(2)$ groups is described over the circle group $\mathbb{T}$ with respect to a specific $R$-matrix $R$. Additionally, the corresponding bosonization is also described.
Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.
The discussions in the present paper arise from exploring intrinsically the structure nature of the quantum $n$-space. A kind of braided category $\Cal {GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$ is…
All deformations of two dimensional centrally extended Galilei group are classified. The corresponding quantum Lie algebras are found.
Quantum matrices $A(R)$ are known for every $R$ matrix obeying the Quantum Yang-Baxter Equations. It is also known that these act on `vectors' given by the corresponding Zamalodchikov algebra. We develop this interpretation in detail,…
We describe a new technique to obtain representations of the braid group B_n from the R-matrix of a quantum deformed algebra of the one dimensional harmonic oscillator. We consider the action of the R-matrix not on the tensor product of…
A review of the multiparametric linear quantum group GL_qr(N), its real forms, its dual algebra U(gl_qr(N)) and its bicovariant differential calculus is given in the first part of the paper. We then construct the (multiparametric) linear…
The quantum double construction of a $q$-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The $R$-matrix thus obtained is compared with the existing literature.
A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…
GL_q(N)- and SO_q(N)-covariant deformations of the completely symmetric/antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices. The precise relation between the…
This paper is the sequel to [HP1] to study the deformed structures and representations of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ associated to the finite dimensional simple Lie algebras $\mg$. An equivalence of the braided…
We consider the possible covariant external algebra structures for Cartan's 1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates: 1. the invariant 1-forms realize an adjoint representation of quantum group; 2. all…
Rickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to…
Quantum superalgebras $su_{q}(m\mid n)$ are studied in the framework of $R$-matrix formalism. Explicit parametrization of $L^{(+)}$ and $L^{(-)}$ matrices in terms of $su_{q}(m\mid n)$ generators are presented. We also show that quantum…
We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum $\mathfrak{sl}_N$, their duals, and their direct sums. We show that the first two…