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. ...

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...

Equivariant one-parameter deformations of associative algebra morphisms

Raj Bhawan Yadav (2023)

Czechoslovak Mathematical Journal

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We introduce equivariant formal deformation theory of associative algebra morphisms. We also present an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal deformation theory of associative algebra morphisms. We discuss some examples of equivariant deformations and use the Maurer-Cartan equation to characterize equivariant deformations.

The garden of quantum spheres

Ludwik Dąbrowski (2003)

Banach Center Publications

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A list of known quantum spheres of dimension one, two and three is presented.