Displaying similar documents to “Construction of the Bethe state for the E τ , η ( SO 3 ) elliptic quantum group.”

Quantum symmetries in noncommutative C*-systems

Marcin Marciniak (1998)

Banach Center Publications

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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...

Quantum isometries and group dual subgroups

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

Annales mathématiques Blaise Pascal

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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

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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.

On quantum weyl algebras and generalized quons

WŁadysŁaw Marcinek (1997)

Banach Center Publications

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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.

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

MaŁgorzata Klimek (1997)

Banach Center Publications

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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.