Journal ArticleDOI
Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
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In this paper, the notion of concrete monoidal W *-category is introduced and investigated, and a generalization of the Tannaka-Krein duality theorem is proved, leading to new examples of compact matrix pseudogroups.Abstract:
The notion of concrete monoidalW
*-category is introduced and investigated. A generalization of the Tannaka-Krein duality theorem is proved. It leads to new examples of compact matrix pseudogroups. Among them we have twistedSU(N) groups denoted byS
μ
U(N). It is shown that the representation theory forS
μ
U(N) is similar to that ofSU(N): irreducible representations are labeled by Young diagrams and formulae for dimensions and multiplicity are the same as in the classical case.read 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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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.
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Introduction to Quantum Groups
P. Podleś,E. Müller +1 more
TL;DR: In this paper, the authors give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz) and recall the basic facts from Hopf (*-) algebra theory, theory of compact (matrix) quantum groups and their actions on compact quantum spaces, and provide the most important examples, including the classification of quantum SL(2)-groups, their real forms and quantum spheres.
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Locally compact quantum groups
Johan Kustermans,Stefaan Vaes +1 more
TL;DR: The theory of locally compact quantum groups that are studied in the framework of operator algebras, i.e., C*-alges and von Neumann alges, is introduced in this paper.
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Free products of compact quantum groups
TL;DR: In this article, the authors construct and study compact quantum groups from free products of C======*-algebras, and discover two mysterious classes of natural compact groups, A====== u¯¯ �(m) and A====== o¯¯ ��(m), which are non-isomorphic to each other for different m's, and are not obtainable by the ordinary quantization method.
References
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Journal ArticleDOI
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.
Journal ArticleDOI
Twisted SU (2) group. An example of a non-commutative differential calculus
TL;DR: 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.