Timeline for Crossed products of A by ℤ: non-stably isomorphic examples

5 events

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Dec 7, 2021 at 15:18	comment	added	C-star-W-star		Right, I see, thanks Jamie also for the nice example! :) Do you maybe wanna have it converted to an answer? I could accept it then.
Dec 7, 2021 at 15:11	comment	added	Jamie Gabe		Stable isomorphism is a very strong equivalence relation! So it is very rare that different automorphisms give you stably isomorphic crossed products. A good example of crossed products by $\mathbb Z$ is the irrational rotation algebras $\mathcal A_\theta = C(\mathbb T) \rtimes_{r(\theta)} \mathbb Z$ for $\theta \in [0,1] \setminus \mathbb Q$, where the automorphism is induced by rotation by $2\pi \theta$. Then $\mathcal A_{\theta_1}$ and $\mathcal A_{\theta_2}$ are (stably) isomorphic if and only if $\theta_1 = \theta_2$ or $\theta_1 = 1-\theta_2$.
Dec 7, 2021 at 15:03	history	edited	C-star-W-star	CC BY-SA 4.0	added 98 characters in body; edited title
Dec 7, 2021 at 15:02	history	edited	LSpice	CC BY-SA 4.0	Double-struck Z in title
Dec 7, 2021 at 14:46	history	asked	C-star-W-star	CC BY-SA 4.0