A classification of inner actions of the Dipper-Donkin quantization GL_2 on the Clifford algebra C(1,3)

Actions of the Dipper-Donkin quantization GL_2 on the Clifford algebra C(1,3)

Following the method already developed for studying the actions of GL_q(2,C) on the Clifford algebra C(1,3) and its quantum invariants (Commun. in Algebra 27, 1843-1878(1999)), we study the action on C(1,3) of the quantum group GL_2 constructed by Dipper and Donkin. We are able of proving that there exists only two non-equivalent cases of actions with nontrivial "perturbation". The space of invariants are trivial in both cases. We also prove that each irreducible finite dimensional algebra representation of the quantum group GL_2, q^m\neq 1, is one dimensional. By studying the cases with zero …

Dipper-Donkin algebra as global symmetry of quantum chains

We analize the role of GL_2, a quantum group constructed by Dipper-Donkin, as a global symmetry for quantum chains, and show the way to construct all possible Hamiltonians for four states quantum chains with GL_2 global symmetry. In doing this, we search all inner actions of GL_2 on the Clifford algebra C(1,3) and show them. We also introduce the corresponding operator algebras, invariants and Hamiltonians, explicitly.

Dipper Donkin Quantized Matrix Algebra and Reflection Equation Algebra at root of unity

In this article the quantized matrix algebras as in the title have been studied at a root of unity. A full classification of simple modules over such quantized matrix algebras of rank $2$ along with a class of finite dimensional indecomposable modules are given.

On quantum GL(n)

The quantum GL(n) of Faddeev-Reshetikhin-Takhtajan and Dipper-Donkin are realized geometrically by using double partial flag varieties. As a consequence, the difference of these two Hopf algebras is caused by a twist of a cocycle in the multiplication.

借助Gröbner-Shirshov基理论建立的量子矩阵代数$D_q(n)$的结构性质

Structural Properties of The Quantized Matrix Algebra $D_q(n)$ Established by Means of Gröbner-Shirshov Basis Theory

本文证明了Dipper和Donkin引入的量子矩阵代数$D_q(n)$及其模的结构性质，可借助Gröbner-Shirshov基理论进行建立与实现。

R-matrix realization of two-parameter quantum group U_{r,s}(gl_n)

We provide a Faddeev-Reshetikhin-Takhtajan's RTT approach to the quantum group Fun(GL_{r,s}(n)) and the quantum enveloping algebra U_{r,s}(gl_n) corresponding to the two-parameter R-matrix. We prove that the quantum determinant det_{r,s}T is a quasi-central element in Fun(GL_{r,s}(n)) generalizing earlier results of Dipper-Donkin and Du-Parshall-Wang. The explicit formulation provides an interpretation of the deforming parameters, and the quantized algebra U_{r,s}(R) is identified to U_{r,s}(gl_n) as the dual algebra. We then construct n-1 quasi-central elements in U_{r,s}(R) which are analogu…