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On quantum weyl algebras and generalized quons

WŁadysŁaw Marcinek (1997)

Banach Center Publications

The model of generalized quons is described in an algebraic way as certain quasiparticle states with statistics determined by a commutation factor on an abelian group. Quantization is described in terms of quantum Weyl algebras. The corresponding commutation relations and scalar product are also given.

On the contraction of the discrete series of S U ( 1 , 1 )

C. Cishahayo, S. De Bièvre (1993)

Annales de l'institut Fourier

It is shown, using techniques inspired by the method of orbits, that each non-zero mass, positive energy representation of the Poincaré group 𝒫 1 , 1 = S O ( 1 , 1 ) s 2 can be obtained via contraction from the discrete series of representations of S U ( 1 , 1 ) .

On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set

Debashish Goswami, Adam Skalski (2012)

Banach Center Publications

Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.

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