69 research outputs found
Index formulas and charge deficiencies on the Landau levels
The notion of charge deficiency from Avron, Seiler, Simon (Charge deficiency,
charge transport and comparison of dimensions, Comm. Math. Phys. 159) is
studied from the view of -theory and is applied to the Landau levels in
\C^n. We calculate the charge deficiencies of the higher Landau levels in
\C^n by means of an Atiyah-Singer type index theorem.Comment: 18 page
A remark on twists and the notion of torsion-free discrete quantum groups
In this paper twists of reduced locally compact quantum groups are studied.
Twists of the dual coaction on a reduced crossed product are introduced and the
twisted dual coactions are proved to satisfy a type of Takesaki-Takai duality.
The twisted Takesaki-Takai duality implies that twists of discrete,
torsion-free quantum groups are torsion-free. Cocycle twists of duals of
semisimple, compact Lie are studied leading to a locally compact quantum group
contained in the Drinfeld-Jimbo algebra which gives a dual notion of Woronowicz
deformations for semisimple, compact Lie groups. These cocycle twists are
proven to be torsion-free whenever the Lie group is simply connected.Comment: 17 pages, to appear in Algebras and Representation Theory,
http://www.springerlink.com/content/u33rr720672598r3
The Pimsner-Voiculescu sequence for coactions of compact Lie groups
The Pimsner-Voiculescu sequence is generalized to a Pimsner-Voiculescu tower
describing the -category equivariant with respect to coactions of a compact
Lie group satisfying the Hodgkin condition. A dual Pimsner-Voiculescu tower is
used to show that coactions of a compact Hodgkin-Lie group satisfy the
Baum-Connes property.Comment: 19 pages, to appear in Mathematica Scandinavic
Equivariant extensions of *-algebras
A bivariant functor is defined on a category of *-algebras and a category of
operator ideals, both with actions of a second countable group , into the
category of abelian monoids. The element of the bivariant functor will be
-equivariant extensions of a *-algebra by an operator ideal under a suitable
equivalence relation. The functor is related with the ordinary -functor
for -algebras defined by Brown-Douglas-Fillmore. Invertibility in this
monoid is studied and characterized in terms of Toeplitz operators with
abstract symbol.Comment: 12 page
Commutator estimates on contact manifolds and applications
This article studies sharp norm estimates for the commutator of
pseudo-differential operators with multiplication operators on closed
Heisenberg manifolds. In particular, we obtain a Calderon commutator estimate:
If is a first-order operator in the Heisenberg calculus and is
Lipschitz in the Carnot-Caratheodory metric, then extends to an
-bounded operator. Using interpolation, it implies sharp weak--Schatten
class properties for the commutator between zeroth order operators and H\"older
continuous functions. We present applications to sub-Riemannian spectral
triples on Heisenberg manifolds as well as to the regularization of a
functional studied by Englis-Guo-Zhang.Comment: 31 pages, improved presentation and additional reference
Spectral triples and finite summability on Cuntz-Krieger algebras
We produce a variety of odd bounded Fredholm modules and odd spectral triples
on Cuntz-Krieger algebras by means of realizing these algebras as "the algebra
of functions on a non-commutative space" coming from a sub shift of finite
type. We show that any odd -homology class can be represented by such an odd
bounded Fredholm module or odd spectral triple. The odd bounded Fredholm
modules that are constructed are finitely summable. The spectral triples are
-summable although their bounded transform, when constructed using the
sign-function, will already on the level of analytic -cycles be finitely
summable bounded Fredholm modules. Using the unbounded Kasparov product, we
exhibit a family of generalized spectral triples, possessing mildly unbounded
commutators, whilst still giving well defined -homology classes.Comment: 67 pages, minor changes in Section 5.1 and 6.
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