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A computation with the Connes-Thom isomorphism | S.Sundar
; | Date: |
2 Mar 2012 | Abstract: | Let $A in M_{n}(mathbb{R})$ be an invertible matrix. Consider the
semi-direct product $mathbb{R}^{n}
times mathbb{Z}$ where $mathbb{Z}$ acts
on $mathbb{R}^{n}$ by matrix multiplication. Consider a strongly continuous
action $(alpha, au)$ of $mathbb{R}^{n}
times mathbb{Z}$ on a
$C^{*}$-algebra $B$ where $alpha$ is a strongly continuous action of
$mathbb{R}^{n}$ and $ au$ is an automorphism. The map $ au$ induces a map
$widetilde{ au}$ on $B
times_{alpha} mathbb{R}^{n}$. We show that, at the
$K$-theory level, $ au$ commutes with the Connes-Thom map if $det(A)>0$ and
anticommutes if $det(A)<0$. As an application, we recompute the $K$-groups of
the Cuntz-Li algebra associated to an integer dilation matrix. | Source: | arXiv, 1203.0383 | Services: | Forum | Review | PDF | Favorites |
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