Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres

Elmar Wagner

Displaying similar documents to “Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres”

Dirac operator on the standard Podleś quantum sphere

Ludwik Dąbrowski, Andrzej Sitarz (2003)

Banach Center Publications

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Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podleś quantum sphere: equivariant representation, chiral grading γ, reality structure J and the Dirac operator D, which has bounded commutators with the elements of the algebra and satisfies the first order condition.

Equivariant Morita equivalences between Podleś spheres

Kenny De Commer (2012)

Banach Center Publications

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We show that the family of Podleś spheres is complete under equivariant Morita equivalence (with respect to the action of quantum SU(2)), and determine the associated orbits. We also give explicit formulas for the actions which are equivariantly Morita equivalent with the quantum projective plane. In both cases, the computations are made by examining the localized spectral decomposition of a generalized Casimir element.

Equivariant spectral triples

Andrzej Sitarz (2003)

Banach Center Publications

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We present the review of noncommutative symmetries applied to Connes' formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries: isospectral (twisted) deformations (including noncommutative torus) and finite spectral triples. ...

The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C∖{0}

Jan Milewski (2007)

Banach Center Publications

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We consider equivariant solutions of Schrödinger equations on C∖{0} with harmonic oscillator potentials. We determine the spaces of equivariant quantum states in three cases: for an isotropic and anisotropic harmonic oscillator potential centered at 0, and for a potential not centered at 0.

Quantum isometry group for spectral triples with real structure.

Goswami, Debashish (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Twisted spectral triples and covariant differential calculi

Ulrich Krähmer, Elmar Wagner (2011)

Banach Center Publications

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Connes and Moscovici recently studied "twisted" spectral triples (A,H,D) in which the commutators [D,a] are replaced by D∘a - σ(a)∘D, where σ is a second representation of A on H. The aim of this note is to point out that this yields representations of arbitrary covariant differential calculi over Hopf algebras in the sense of Woronowicz. For compact quantum groups, H can be completed to a Hilbert space and the calculus is given by bounded operators. At the end, we discuss an explicit...