Twisted SU (2) group. An example of a non-commutative differential calculus
TLDR
In this paper, a C*-algebre A engendree par deux elements α et γ satisfaisant une relation de commutation simple dependante de ν is presented.Abstract:
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 νread more
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Compact matrix pseudogroups
TL;DR: The compact matrix pseudogroup as mentioned in this paper is a non-commutative compact space endowed with a group structure, and the existence and uniqueness of the Haar measure is proved and orthonormality relations for matrix elements of irreducible representations are derived.
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Quantum field theory on noncommutative spaces
TL;DR: In this article, a pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity.
Book ChapterDOI
Quantization of Lie Groups and Lie Algebras
TL;DR: The quantum inverse scattering method for solving nonlinear equations of evolution, the quantum theory of magnets, the method of commuting transfer-matrices in classical statistical mechanics, and factorizable scattering theory as discussed by the authors emerged as a natural development of the various directions in mathematical physics.
Journal ArticleDOI
On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q
TL;DR: The quantum group SU(2)q is discussed in this paper by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose.
Journal ArticleDOI
Differential calculus on compact matrix pseudogroups (quantum groups)
TL;DR: In this paper, a general theory of non-commutative differential geometry on quantum groups is developed, where bicovariant bimodules as objects analogous to tensor bundles over Lie groups are studied.
References
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Pseudospaces, pseudogroups and pontriagin duality
TL;DR: The main result of the Gelfand Naima-k theory of commutative C-algebras can be stated in the following way as mentioned in this paper : the category of non-convex C−algebbras with unity and unital C'-homomorphisms is dual to the categories of compact topological spaces and continuous maps.
Journal ArticleDOI
C*‐Algèbres de Hopf et C*‐Algèbres de Kac
TL;DR: In this paper, the definitions des C*-algebres de Hopf et de Kac ainsi que certaines proprietes are discussed. And the action d'une C * algebre de KAC sur une C * -algebre C r *(G) is defined.
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