18 citations · 34 across the 10 of their papers we have counts for
10 papers
Quantum groups of Lie colour algebras fulfilling the Cartan-Weyl paradigm
R. B. Zhang
Let Gamma be an additive abelian group with a commutative factor omega. We describe the simple and untwisted affine Lie colour algebras which admit a Cartan - Weyl description. For…
Invariants and representations of the -graded general linear Lie -algebras
R. B. Zhang
There is considerable current interest in applications of generalised Lie algebras graded by an abelian group with a commutative factor . This calls for a systematic develop…
A polar Brauer category and Lie superalgebra representations
G. I. Lehrer, R. B. Zhang
We introduce a diagram category, study its structure, and investigate some of its applications to the representation theory of Lie algebras and Lie superalgebras. The morphisms of…
Drinfeld realisations of quantum affine superalgebras
Ying Xu, R. B. Zhang
We construct Drinfeld realisations for the quantum affine superalgebras associated with the osp(1|2n)^{(1)}, Sl(1|2n)^{(2)} and osp(2|2n)^{(2)} series of affine Lie superalgebras.
A noncommutative geometric approach to the quantum structure of spacetime
R. B. Zhang, Xiao Zhang
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dim…
Generalised Verma modules for the orthosymplectic Lie superalgebra osp(k|2)
Yucai Su, R. B. Zhang
The composition factors and their multiplicities are determined for generalised Verma modules over the orthosymplectic Lie superalgebra osp(k|2). The results enable us to obtain ex…
[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]
[Pi-Gang Luan, H. C. Lee, R. B. Zhang]
We study the Hopf algebra structure and the highest weight representation of a multiparameter version of . The commutation relations as well as other Hopf algebra maps…
Quantum Group Duality and the Cuntz Algebra
A. L. Carey, A. Paolucci, R. B. Zhang
The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra , and the structure of a co-module algebra over…
Bott - Borel - Weil Construction For Quantum Supergroup Uq(gl(m|n))
R. B. Zhang
The finite dimensional irreducible representations of the quantum supergroup are constructed geometrically using techniques from the Bott - Borel - Weil theory and v…
Finite dimensional representations of at arbitrary
R. B. Zhang
A method is developed to construct irreducible representations(irreps) of the quantum supergroup in a systematic fashion. It is shown that every finite dimensional ir…