40 research outputs found
A C*-Algebraic Model for Locally Noncommutative Spacetimes
Locally noncommutative spacetimes provide a refined notion of noncommutative
spacetimes where the noncommutativity is present only for small distances. Here
we discuss a non-perturbative approach based on Rieffel's strict deformation
quantization. To this end, we extend the usual C*-algebraic results to a
pro-C*-algebraic framework.Comment: 13 pages, LaTeX 2e, no figure
On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1)
In a previous paper, we showed how one can obtain from the action of a
locally compact quantum group on a type I-factor a possibly new locally compact
quantum group. In another paper, we applied this construction method to the
action of quantum SU(2) on the standard Podles sphere to obtain Woronowicz'
quantum E(2). In this paper, we will apply this technique to the action of
quantum SU(2) on the quantum projective plane (whose associated von Neumann
algebra is indeed a type I-factor). The locally compact quantum group which
then comes out at the other side turns out to be the extended SU(1,1) quantum
group, as constructed by Koelink and Kustermans. We also show that there exists
a (non-trivial) quantum groupoid which has at its corners (the duals of) the
three quantum groups mentioned above.Comment: 35 page
BMO spaces associated with semigroups of operators
We study BMO spaces associated with semigroup of operators and apply the
results to boundedness of Fourier multipliers. We prove a universal
interpolation theorem for BMO spaces and prove the boundedness of a class of
Fourier multipliers on noncommutative Lp spaces for all 1 < p < \infty, with
optimal constants in p.Comment: Math An
Frobenius structures over Hilbert C*-modules
We study the monoidal dagger category of Hilbert C*-modules over a
commutative C*-algebra from the perspective of categorical quantum mechanics.
The dual objects are the finitely presented projective Hilbert C*-modules.
Special dagger Frobenius structures correspond to bundles of uniformly
finite-dimensional C*-algebras. A monoid is dagger Frobenius over the base if
and only if it is dagger Frobenius over its centre and the centre is dagger
Frobenius over the base. We characterise the commutative dagger Frobenius
structures as finite coverings, and give nontrivial examples of both
commutative and central dagger Frobenius structures. Subobjects of the tensor
unit correspond to clopen subsets of the Gelfand spectrum of the C*-algebra,
and we discuss dagger kernels.Comment: 35 page