145 citations · 1.4k across the 82 of their papers we have counts for
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Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras
Mark D. Gould, Phillip S. Isaac, Jason L. Werry
We develop explicit formulae for the eigenvalues of various invariants for highest weight irreducible representations of the quantum supergroup . The techniques emplo…
Local Quasitriangular Hopf Algebras
Shouchuan Zhang, Mark D. Gould, Yao-Zhong Zhang
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yan…
Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]
K. A. Dancer, M. D. Gould, J. Links
Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal -matrix} in the tensor product algebra which satisfies the Yang-Baxter equatio…
Eigenvalues of Casimir invariants for Uq[osp(m|n)]
K. A. Dancer, M. D. Gould, J. Links
For each quantum superalgebra with , an infinite family of Casimir invariants is constructed. This is achieved by using an explicit form for the Lax operator.…
Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(m|n)]
K. A. Dancer, M. D. Gould, J. Links
Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-tr…
Some Twisted Results
M. D. Gould, T. Lekatsas
The Drinfeld twist for the opposite quasi-Hopf algebra is determined and is shown to be related to the (second) Drinfeld twist. The twisted Drinfeld twist is investigated. In the q…
A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)
Yao-Zhong Zhang, Mark D. Gould
Representations of the non-semisimple superalgebra in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All…
Vertex Operators, Screen Currents and Correlation Functions at Arbitrary Level
Yao-Zhong Zhang, Mark D. Gould
Bosonized q-vertex operators related to the 4-dimensional evaluation modules of the quantum affine superalgebra are constructed for arbitrary level , wher…
Twisted Quantum Affine Superalgebra and New Invariant R-matrices
Mark D. Gould, Yao-Zhong Zhang
The minimal irreducible representations of , i.e. those irreducible representations that are also irreducible under are investigated and shown to be a…
Twisting invariance of link polynomials derived from ribbon quasi-Hopf algebras
J. R. Links, M. D. Gould, Y. -Z. Zhang
The construction of link polynomials associated with finite dimensional representations of ribbon quasi-Hopf algebras is discussed in terms of the formulation of an appropriate Mar…
On Quasi-Hopf superalgebras
Mark D. Gould, Yao-Zhong Zhang, Phillip S. Isaac
In this work we investigate several important aspects of the structure theory of the recently introduced quasi-Hopf superalgebras (QHSAs), which play a fundamental role in knot the…
Casimir Invariants from Quasi-Hopf (Super)algebras
Mark. D. Gould, Yao-Zhong Zhang, Phillip S. Isaac
We show how to construct, starting from a quasi-Hopf (super)algebra, central elements or Casimir invariants. We show that these central elements are invariant under quasi-Hopf twis…
Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups
Yao-Zhong Zhang, Mark D. Gould
We introduce the quasi-Hopf superalgebras which are graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-tr…