## 1,357 Citations

Lectures on Hopf Algebras, Quantum Groups and Twists

- Mathematics
- 2007

Lead by examples we introduce the notions of Hopf algebra and quantum group. We study their geometry and in particular their Lie algebra (of left invariant vectorfields). The examples of the quantum…

Representation of quantum algebras arising from non-compact quantum groups : quantum orbit method and super-tensor products

- Mathematics
- 1996

In this thesis, I present a version of the quantum orbit method which provides a geometrical construction of the irreducible *-representations of the quantum universal enveloping algebras for the…

Quantum groups and deformation quantization: Explicit approaches and implicit aspects

- Mathematics
- 2004

Deformation quantization, which gives a development of quantum mechanics independent of the operator algebra formulation, and quantum groups, which arose from the inverse scattering method and a…

Quantum group gauge theory on quantum spaces

- Mathematics, Physics
- 1992

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including aq-deformed Dirac monopole on the quantum sphere of Podles with quantum differential structure coming…

Quantization of the category of linear spaces

- Mathematics
- 1997

We define generalized bialgebras and Hopf algebras and on this basis we introduce quantum categories and quantum groupoids. The quantization of the category of linear (super)spaces is constructed. We…

Elementary Introduction to Quantum Groups

- Mathematics
- 1993

In this elementary survey we introduce and study basic properties of quantum groups — new mathematical objects emerged from the theory of quantum integrable systems. Their classical counterpart —…

Topological Hopf Algebras, Quantum Groups and Deformation Quantization

- MathematicsHopf Algebras in Noncommutative Geometry and Physics
- 2019

After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologi es on Hopf algebras associated with…

Linearly Recursive Sequences, Witt Algebras and Quantum Groups

- Mathematics
- 1993

We discuss some topics related to quantum groups. See[D] for general background on quantum groups, and [S] for Hopf algebras. In section 1, we discuss Lie bialgebra structures on Witt and Virasoro…

Induced Extended Calculus On The Quantum Plane

- Mathematics, Physics
- 2007

The non-commutative differential calculus on quantum groups can be extended by introducing, in analogy with the classical case, inner product operators and Lie derivatives. For the case of GLq(n) we…

## References

SHOWING 1-10 OF 24 REFERENCES

The Yangians, Bethe Ansatz and combinatorics

- Mathematics
- 1986

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…

Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

- Mathematics, Physics
- 1979

Representations of quantum groups and a q-analogue of orthogonal polynomials

- Mathematics
- 1988

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

- Mathematics
- 1986

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

- Physics
- 1988

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…

Twisted SU (2) group. An example of a non-commutative differential calculus

- Mathematics
- 1987

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

- Mathematics
- 1986

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

- Mathematics
- 1985

On explique les proprietes de Poisson des transformations d'habillage en theorie des solitons