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location University of Maryland
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seen Aug 14 at 22:01

I am a PhD student at the University of Maryland working on tilings and their relationship to harmonic analysis and noncommutative geometry.


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)
deleted 1 character in body
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)
added 6 characters in body
Aug
4
comment 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
comment 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)
Jul
2
awarded  Curious
Jun
10
awarded  Yearling
Jun
10
accepted C* algebras of Almost Periodic Functions
Jun
10
answered C* algebras of Almost Periodic Functions
Jun
6
revised C* algebras of Almost Periodic Functions
added 10 characters in body
Jun
6
asked C* algebras of Almost Periodic Functions
Jun
3
accepted Is any finite collection of points contained in a cut and project set with $\mathbb{R}^d$ as internal space?
Jun
3
comment Is any finite collection of points contained in a cut and project set with $\mathbb{R}^d$ as internal space?
Thanks for the idea! That's what I was looking for. Hopefully I can prove that lemma.
May
20
comment Is any finite collection of points contained in a cut and project set with $\mathbb{R}^d$ as internal space?
Thanks for the response, however I was trying to get at something slightly different than your answer. I wanted specifically that the internal space was R^n and not a different LCAG. I'm not concerned with uniqueness, but simply with whether we can realize any finite set as a subset of a model set where the internal space is R^n. I think this is possible, but I haven't seen a proof anywhere.
Jan
14
revised Is any finite collection of points contained in a cut and project set with $\mathbb{R}^d$ as internal space?
edited body
Jan
14
asked Is any finite collection of points contained in a cut and project set with $\mathbb{R}^d$ as internal space?
Dec
20
comment When is a collection of exponentials dense in $L^2(K), |K|<\infty$
This book seems concentrated on the $d=1$ case. Has a similar analysis been done in higher dimensions?
Dec
20
awarded  Critic