A two-parameter quantization of osp(4/2)

@article{Zhang1992ATQ,
  title={A two-parameter quantization of osp(4/2)},
  author={Rui-bin Zhang},
  journal={Journal of Physics A},
  year={1992},
  volume={25}
}
  • Rui-bin Zhang
  • Published 21 August 1992
  • Mathematics
  • Journal of Physics A
A two-parameter deformation of the universal algebra of osp(4/2) is carried out, yielding a Z2-graded Hopf algebra with a bijective antipode. This Hopf algebra depends on the extra parameter in both its algebraic and coalgebraic structures, and also admits nontrivial finite-dimensional irreps at arbitrary deformation parameters. 
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References

SHOWING 1-10 OF 13 REFERENCES
Universal R-matrix of the quantum superalgebra osp(2 | 1)
A quantum analogue of the simplest superalgebra osp(2 | 1) and its finite-dimensional, irreducible representations are found. The corresponding constant solution to the Yang-Baxter equation is…
The two-parameter deformation ofGL(2), its differential calculus, and Lie algebra
The Yang-Baxter equation is solved in two dimensions giving rise to a two-parameter deformation ofGL(2). The transformation properties of quantum planes are briefly discussed. Non-central determinant…
Consistent multiparameter quantisation of GL(n)
The author describes a manifold of quantum group structures on the vector space of the universal enveloping algebra of gl(n) and on its dual, the space of polynomials in n2 variables. The dimension…
Aq-difference analogue of U(g) and the Yang-Baxter equation
Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced. Its structure and representations are studied in the simplest case g=sl(2). It is then applied…
The multiparametric deformation ofGL(n) and the covariant differential calculus on the quantum vector space
AbstractAn(n−1)/2+1 parameter, solution of the Yang Baxter equation is presented giving rise to the quantum Group $$GL_{X;q_{ij} } (n)$$ . Determinant and inverse are constructed. The group acts…
Solution of the graded Yang-Baxter equation associated with the vector representation of Uq(osp(M/2n))
Multiparameter associative generalizations of canonical commutation relations and quantized planes
Quantum lie superalgebras and q-oscillators
Multiparametric quantum deformation of the general linear supergroup
In the work L. D. Faddeev and his collaborators, and subsequently V. G. Drinfeld, M. Jimbo, S. L. Woronowicz, a new class of Hopf algebras was constructed. They can be considered as one-parametric…
The Pokrovski-Talapov Phase Transitions and Quantum Groups
We show that the XY quantum chain in a magnetic field is invariant under a two parameter deformation of the SU(1/1) superalgebra. One is led to an extension of the braid group and the Hecke algebras…
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