Quantization of Lie Groups and Lie Algebras

  title={Quantization of Lie Groups and Lie Algebras},
  author={Ludwig D. Faddeev and Nicolai Reshetikhin and Leon A. Takhtajan},
Lectures on Hopf Algebras, Quantum Groups and Twists
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
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
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
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
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
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
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
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
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


The Yangians, Bethe Ansatz and combinatorics
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
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
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