Timeline for Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
Current License: CC BY-SA 3.0
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| Aug 6, 2014 at 13:56 | history | edited | mkreisel | CC BY-SA 3.0 |
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| Aug 4, 2014 at 17:21 | history | edited | mkreisel | CC BY-SA 3.0 |
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| Aug 4, 2014 at 17:19 | comment | added | mkreisel | 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, 2014 at 15:59 | vote | accept | John N. | ||
| Aug 4, 2014 at 14:47 | comment | added | John N. | Ok, thanks for the asnwer. I'll try to read Luef's paper. | |
| Aug 4, 2014 at 14:42 | comment | added | mkreisel | 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, 2014 at 14:19 | comment | added | John N. | mkreisel: Thank you for the answer. I have one more question. You said that for the 2-torus the above action gives the non trivial class of the $K_0-$group and when $\theta$ is irrational the associated projection is equivalent to the Rieffel projection. What happen $\theta$ is rational? Is there and explicit description of the associated projection? Thank you again for the help. | |
| Aug 4, 2014 at 13:50 | history | answered | mkreisel | CC BY-SA 3.0 |