Quantization of Lie Groups and Lie Algebras

@inproceedings{Faddeev1987QuantizationOL,
  title={Quantization of Lie Groups and Lie Algebras},
  author={Ludwig D. Faddeev and Nicolai Reshetikhin and Leon A. Takhtajan},
  year={1987}
}
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1,357 Citations

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References

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An axiomatic definition of a quantum monodromy matrix and the representations of its corresponding Hopf algebra are discussed. The connection between the quantum inverse transform method and the…
Trigonometric solutions of triangle equations and classical lie algebras
Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
Representations of quantum groups and a q-analogue of orthogonal polynomials
The Peter-Weyl theorem for SμU(2) of Woronowicz is shown in an explicit form and a q-analogue of certain orthogonal polynomials is realized as the spherical functions for SμU(2) On presente le…
A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation
We study for g=g[(N+1) the structure and representations of the algebra Ŭ(g), a q-analogue of the universal enveloping algebra U(g). Applying the result, we construct trigonometric solutions of the…
Liouville model on the lattice
Liouville equation is put on the lattice in a completely integrable way. The classical version is investigated in details and a lattice deformation of the Virasoro algebra is obtained. The quantum…
Quantum deformations of certain simple modules over enveloping algebras
Twisted SU (2) group. An example of a non-commutative differential calculus
Pour un nombre ν de l'intervalle [−1, 1], on introduit et on etudie une C*-algebre A engendree par deux elements α et γ satisfaisant une relation de commutation simple dependante de ν
QuantumR matrix for the generalized Toda system
We report the explicit form of the quantumR matrix in the fundamental representation for the generalized Toda system associated with non-exceptional affine Lie algebras.
Dressing transformations and Poisson group actions
On explique les proprietes de Poisson des transformations d'habillage en theorie des solitons
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