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Spectral Triples
, 2015
"... A spectral triple is a family (H,A,D), such that • H is a Hilbert space • D is a selfadjoint operator onH with compact resolvent. • A is a unital C∗algebra with a faithful representation pi intoH • There is a core D in the domain of D, and a dense ∗subalgebra A0 ⊂ A such that if a ∈ A0 thenpi(a)D ..."
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A spectral triple is a family (H,A,D), such that • H is a Hilbert space • D is a selfadjoint operator onH with compact resolvent. • A is a unital C∗algebra with a faithful representation pi intoH • There is a core D in the domain of D, and a dense ∗subalgebra A0 ⊂ A such that if a ∈ A0 thenpi
Equivariant 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 Ktheory, homology, equ ..."
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Cited by 10 (5 self)
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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 Ktheory, homology
Moyal planes are spectral triples
, 2003
"... Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory, the spaces R 2N endowed with Moyal products are intensively investigated. Some physical applications, ..."
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Cited by 75 (20 self)
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Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory, the spaces R 2N endowed with Moyal products are intensively investigated. Some physical applications
EXTENSIONS AND DEGENERATIONS OF SPECTRAL TRIPLES
, 709
"... Abstract. For a unital C*algebra A, which is equipped with a spectral triple (A, H, D) and an extension T of A by the compacts, we construct a two parameter family of spectral triples (At, K, Dα,β) associated to T. Using Rieffel’s notation of quantum GromovHausdorff distance between compact quantu ..."
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Cited by 2 (0 self)
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Abstract. For a unital C*algebra A, which is equipped with a spectral triple (A, H, D) and an extension T of A by the compacts, we construct a two parameter family of spectral triples (At, K, Dα,β) associated to T. Using Rieffel’s notation of quantum GromovHausdorff distance between compact
Discrete Spectral Triples and Their Symmetries
 J. Math. Phys
, 1996
"... We classify 0dimensional spectral triples over complex and real algebras and provide some general statements about their di#erential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf algebra structure of the finite algebra. We discuss examples of co ..."
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Cited by 39 (1 self)
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We classify 0dimensional spectral triples over complex and real algebras and provide some general statements about their di#erential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf algebra structure of the finite algebra. We discuss examples
EXTENDED SPECTRAL TRIPLES AND DEFORMATIONS
, 709
"... Abstract. For a unital C*algebra A, which is equipped with a spectral triple (A, H, D) and a Toeplitz extension, T, of A by the compacts, we construct a two parameter family of spectral triples (At, K, D (α,β)) associated to T. Using Rieffel’s notation, the family of spectral triples induce a two p ..."
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Abstract. For a unital C*algebra A, which is equipped with a spectral triple (A, H, D) and a Toeplitz extension, T, of A by the compacts, we construct a two parameter family of spectral triples (At, K, D (α,β)) associated to T. Using Rieffel’s notation, the family of spectral triples induce a two
CLASSIFICATION OF FINITE SPECTRAL TRIPLES
, 1996
"... It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in terms of matrices and classified using diagrams. When tensorized ..."
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It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in terms of matrices and classified using diagrams. When
Critical dimension of Spectral Triples
, 2008
"... It is open the possibility of imposing requisites to the quantisation of Spectral Triples in such a way that a critical dimension D=26 appears. From [1] it is known that commutative spectral triples contain the Einstein Hilbert action, which is extracted by using the Wodziski residue over D / −2 D ..."
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It is open the possibility of imposing requisites to the quantisation of Spectral Triples in such a way that a critical dimension D=26 appears. From [1] it is known that commutative spectral triples contain the Einstein Hilbert action, which is extracted by using the Wodziski residue over D / −2 D
κDeformation and Spectral Triples
, 2011
"... The aim of the paper is to answer the following question: does κdeformation fit into the framework of noncommutative geometry in the sense of spectral triples? Using a compactification of time, we get a discrete version of κMinkowski deformation via C∗algebras of groups. The dynamical system of ..."
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The aim of the paper is to answer the following question: does κdeformation fit into the framework of noncommutative geometry in the sense of spectral triples? Using a compactification of time, we get a discrete version of κMinkowski deformation via C∗algebras of groups. The dynamical system
Results 1  10
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