bio | website | |
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location | University of Maryland | |
age | ||
visits | member for | 2 years, 8 months |
seen | Dec 19 at 23:03 | |
stats | profile views | 293 |
I am a PhD student at the University of Maryland working on tilings and their relationship to harmonic analysis and noncommutative geometry.
Dec 7 |
comment |
Can any Delone set be approximated by a model set?
I make no comment on what the spelling ought to be, nor do I have any power over how it is generally used, as this type of choice is made over time, often somewhat arbitrarily, by the community at large... |
Dec 7 |
comment |
Can any Delone set be approximated by a model set?
The vast majority of recent papers in the theory of tilings use the spelling Delone, although the spelling Delaunay can be found in some older papers. Examples: arxiv.org/abs/1411.0578, arxiv.org/abs/1401.3725, arxiv.org/abs/1407.1787. |
Dec 7 |
comment |
Can any Delone set be approximated by a model set?
I think that's right? I've seen both spellings in papers before. |
Dec 6 |
revised |
Can any Delone set be approximated by a model set?
added 216 characters in body |
Dec 6 |
comment |
Can any Delone set be approximated by a model set?
Edited to include complete definition of $\Lambda_W.$ A cut and project set (or model set) is any set of the same form as $\Lambda_W$ above, where we can vary the lattice $L,$ the subspace $H,$ and the window $W,$ so long as $H$ remains in irrational position w.r.t. $L.$ A Meyer set is any subset of a model set. |
Dec 6 |
revised |
Can any Delone set be approximated by a model set?
added 135 characters in body |
Dec 6 |
asked | Can any Delone set be approximated by a model set? |
Sep 29 |
answered | Projective modules over noncommutative tori? |
Sep 26 |
comment |
Morita Equivalence of Full Corners in $C^*$-algebras
Thanks Alain - suppose I'm given a projection in $\mathcal{A}$ or in $M_n(\mathcal{A}).$ Based on this method, is it easy to construct a projection in $M_k(\mathcal{B})$ that it gets mapped to under this isomorphism? |
Sep 26 |
asked | Morita Equivalence of Full Corners in $C^*$-algebras |
Sep 24 |
awarded | Autobiographer |
Sep 2 |
awarded | Enlightened |
Sep 2 |
awarded | Nice Answer |
Aug 6 |
revised |
Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
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Aug 4 |
revised |
K-theory for the $C^*-$algebra of the continuous functions on the $2-$torus and the Bott projection
added 1071 characters in body |
Aug 4 |
answered | K-theory for the $C^*-$algebra of the continuous functions on the $2-$torus and the Bott projection |
Aug 4 |
revised |
Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
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Aug 4 |
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Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
Look at Theorem 3.6 in Luef's paper. This gives an explicit construction of such projections, which is explicit in the sense that it gives a power series type expansion in terms of products of the generators of the rotation algebra. This is somewhat different than the presentation of Rieffel's original projection, which used functional calculus. |
Aug 4 |
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Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
In general, given a finitely generated projective module with a standard module frame, there is a procedure for constructing the associated projection. Luef's paper above essentially gives what you're asking for, although it is phrased partially in frame theoretic language since this is the easiest way to describe standard module frames for these modules. |
Aug 4 |
answered | Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra) |