Displaying similar documents to “Quantum Painlevé equations: from continuous to discrete.”

Quantum isometries and group dual subgroups

Teodor Banica, Jyotishman Bhowmick, Kenny De Commer (2012)

Annales mathématiques Blaise Pascal

Similarity:

We study the discrete groups Λ whose duals embed into a given compact quantum group, Λ ^ ⊂ G . In the matrix case G ⊂ U n + the embedding condition is equivalent to having a quotient map Γ U → Λ , where F = { Γ U ∣ U ∈ U n } is a certain family of groups associated to G . We develop here a number of techniques for computing F , partly inspired from Bichon’s classification of group dual subgroups Λ ^ ⊂ S n + . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot...

Statistics and quantum group symmetries

Gaetano Fiore, Peter Schupp (1997)

Banach Center Publications

Similarity:

Using 'twisted' realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.

Quantum symmetries in noncommutative C*-systems

Marcin Marciniak (1998)

Banach Center Publications

Similarity:

We introduce the notion of a completely quantum C*-system (A,G,α), i.e. a C*-algebra A with an action α of a compact quantum group G. Spectral properties of completely quantum systems are investigated. In particular, it is shown that G-finite elements form the dense *-subalgebra of A. Furthermore, properties of ergodic systems are studied. We prove that there exists a unique α-invariant state ω on A. Its properties are described by a family of modular operators σ z z ∈ ℂ acting on . It turns...

The symmetry algebra and conserved Currents for Klein-Gordon equation on quantum Minkowski space

MaŁgorzata Klimek (1997)

Banach Center Publications

Similarity:

The symmetry operators for Klein-Gordon equation on quantum Minkowski space are derived and their algebra is studied. The explicit form of the Leibniz rules for derivatives and variables for the case Z=0 is given. It is applied then with symmetry operators to the construction of the conservation law and the explicit form of conserved currents for Klein-Gordon equation.

On quantum weyl algebras and generalized quons

WŁadysŁaw Marcinek (1997)

Banach Center Publications

Similarity:

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.