Results 1 to 10 of about 2,084 (42)
Modular Theory, Non-Commutative Geometry and Quantum Gravity [PDF]
, 2010 This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A.
Bertozzini, Paolo +2 more
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Orbit Representations from Linear mod 1 Transformations [PDF]
, 2012 We show that every point $x_0\in [0,1]$ carries a representation of a $C^*$-algebra that encodes the orbit structure of the linear mod 1 interval map $f_{\beta,\alpha}(x)=\beta x +\alpha$.
Martins, Nuno +2 more
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A $P$-Adic Spectral Triple [PDF]
, 2014 We construct a spectral triple for the C$^*$-algebra of continuous functions on the space of $p$-adic integers by using a rooted tree obtained from coarse-grained approximation of the space, and the forward derivative on the tree. Additionally, we verify
Klimek, Slawomir +2 more
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Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs [PDF]
, 2011 We study Gelfand pairs for locally compact quantum groups. We give an operator algebraic interpretation and show that the quantum Plancherel transformation restricts to a spherical Plancherel transformation.
Caspers, Martijn
core +4 more sources
Quantum Isometry Groups of Noncommutative Manifolds Obtained by Deformation Using Dual Unitary 2-Cocycles [PDF]
, 2014 It is proved that the (volume and orientation-preserving) quantum isometry group of a spectral triple obtained by deformation by some dual unitary 2-cocycle is isomorphic with a similar twist-deformation of the quantum isometry group of the original ...
Goswami, Debashish, Joardar, Soumalya
core +3 more sources
Classification of non-Kac compact quantum groups of SU(n) type [PDF]
, 2015 We classify up to isomorphism all non-Kac compact quantum groups with the same fusion rules and dimension function as $SU(n)$. For this we first prove, using categorical Poisson boundary, the following general result.
Neshveyev, Sergey, Yamashita, Makoto
core +2 more sources
Curved Noncommutative Tori as Leibniz Quantum Compact Metric Spaces
, 2015 We prove that curved noncommutative tori, introduced by Dabrowski and Sitarz, are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the commutant of the quantum tori in the ...
Connes A. +18 more
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Poisson boundaries of monoidal categories
, 2017 Given a rigid C*-tensor category C with simple unit and a probability measure $\mu$ on the set of isomorphism classes of its simple objects, we define the Poisson boundary of $(C,\mu)$.
Neshveyev, Sergey, Yamashita, Makoto
core +1 more source
Quantum Isometry Group for Spectral Triples with Real Structure [PDF]
, 2010 Given a spectral triple of compact type with a real structure in the sense of [Dabrowski L., J. Geom. Phys. 56 (2006), 86-107] (which is a modification of Connes' original definition to accommodate examples coming from quantum group theory) and ...
Goswami, Debashish
core +6 more sources
Canonical tensor product subfactors
, 1999 Canonical tensor product subfactors (CTPS's) describe, among other things, the embedding of chiral observables in two-dimensional conformal quantum field theories.
Rehren, K. -H.
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