Torus Equivariant Spectral Triples for Odd-Dimensional Quantum Spheres Coming from C *-Extensions
نویسندگان
چکیده
منابع مشابه
Torus equivariant spectral triples for odd dimensional quantum spheres coming from C-extensions
The torus group (S) has a canonical action on the odd dimensional sphere S q . We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on that space and equivariant with respect to that action. This characterization gives a construction of an optimum family of equivariant spectral triples having nontrivial K-homology cla...
متن کاملEquivariant spectral triples for SUq(l + 1) and the odd dimensional quantum spheres
We formulate the notion of equivariance of an operator with respect to a covariant representation of a C∗-dynamical system. We then use a combinatorial technique used by the authors earlier in characterizing spectral triples for SUq(2) to investigate equivariant spectral triples for two classes of spaces: the quantum groups SUq(l+1) for l > 1, and the odd dimensional quantum spheres S q of Vaks...
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Abstract The quantum group SUq(l + 1) has a canonical action on the odd dimensional sphere S q . All odd spectral triples acting on the L2 space of S 2l+1 q and equivariant under this action have been characterized. This characterization then leads to the construction of an optimum family of equivariant spectral triples having nontrivial K-homology class. These generalize the results of Chakrab...
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The odd dimensional quantum sphere S q is a homogeneous space for the quantum group SUq(l + 1). A generic equivariant spectral triple for S 2l+1 q on its L2 space was constructed by Chakraborty & Pal in [4]. We prove regularity for that spectral triple here. We also compute its dimension spectrum and show that it is simple. We give detailed construction of its smooth function algebra and some r...
متن کاملEquivariant Spectral Triples
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...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2007
ISSN: 0377-9017,1573-0530
DOI: 10.1007/s11005-007-0149-z