On the K-theory of crossed product C*-algebras by actions of Z^n

Wir untersuchen die K-Theorie von verschränkten Produkt C*-Algebren mit Wirkungen von Z^n und mit besonderem Fokus auf den Fall n=2. Zu einer Z^2-Wirkung auf einer C*-Algebra A assoziieren wir einen Gruppenhomomorphismus zwischen gewissen Subquotienten der K-Theorie von A, der, zusammen mit der K-Theorie von A und der induzierten Wirkung auf K-Theorie, die K-Theorie des verschränkten Produktes bis auf Gruppenerweiterungsprobleme festlegt. Wir präsentieren Beispiele von Z^2-Wirkungen für die dieser Homomorphismus nicht-trivial ist. Für beliebiges n untersuchen wir die Differentiale einer Spektralsequenz, die auf Kasparov zurückgeht und gegen die K-Theorie des zugehörigen verschränkten Produktes konvergiert. Wir zeigen, dass für n=2 das Differential auf der E_2-Seite mit dem oben erwähnten Homomorphismus übereinstimmt. Für beliebiges n setzen wir das Differential auf der E_2-Seite mit den zu den natürlichen Z^2-Unterwirkungen assoziierten Homomorphismen in Verbindung.We investigate the K-theory of crossed product C*-algebras by actions of Z^n with emphasis on the case n=2. Given a Z^2-action on a C*-algebra A, we define a homomorphism between certain subquotients of the K-theory of A, which, together with the K-theory of A and the induced action in K-theory, determines the K-theory of the crossed product up to group extension problems. We present instances of Z^2-actions whose associated obstruction homomorphisms are non-trivial. For arbitrary n, we investigate the differentials of a spectral sequence due to Kasparov, which converges to the K-theory of the associated crossed product. For n=2, we identify the differential on the E_2-term with the abovementioned homomorphism. Moreover, for arbitrary n, we relate the differential on the E_2-term with the homomorphisms associated with the natural Z^2-subactions.<br

Cartan subalgebras and the UCT problem, II

We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF algebra tensorially. More concretely, we prove that for such an action there exists an inverse semigroup of homogeneous partial isometries that generates the ambient C*-algebra and whose idempotent semilattice generates a Cartan subalgebra. We prove a similar result for actions of finite cyclic groups with the Rokhlin property on UCT Kirchberg algebras absorbing a suitable UHF algebra. These results rely on a new construction of Cartan subalgebras in certain inductive limits of Cartan pairs. We also provide a characterisation of the UCT problem in terms of finite order automorphisms, Cartan subalgebras and inverse semigroups of partial isometries of the Cuntz algebra $\mathcal{O}_2$. This generalizes earlier work of the authors.Comment: minor revisions; final version, accepted for publication in Math. Ann.; 26 page

Rokhlin Dimension for Flows

This research was supported by GIF Grant 1137/2011, SFB 878 Groups, Geometry and Actions and ERC Grant No. 267079. Part of the research was conducted at the Fields institute during the 2014 thematic program on abstract harmonic analysis, Banach and operator algebras, and at the Mittag–Leffler institute during the 2016 program on Classification of Operator Algebras: Complexity, Rigidity, and Dynamics.Peer reviewedPostprin

Forward modeling of collective Thomson scattering for Wendelstein 7-X plasmas: Electrostatic approximation

In this paper, we present a method for numerical computation of collective Thomson scattering (CTS). We developed a forward model, eCTS, in the electrostatic approximation and benchmarked it against a full electromagnetic model. Differences between the electrostatic and the electromagnetic models are discussed. The sensitivity of the results to the ion temperature and the plasma composition is demonstrated. We integrated the model into the Bayesian data analysis framework Minerva and used it for the analysis of noisy synthetic data sets produced by a full electromagnetic model. It is shown that eCTS can be used for the inference of the bulk ion temperature. The model has been used to infer the bulk ion temperature from the first CTS measurements on Wendelstein 7-X

Towards a new image processing system at Wendelstein 7-X: From spatial calibration to characterization of thermal events

Wendelstein 7-X (W7-X) is the most advanced fusion experiment in the stellarator line and is aimed at proving that the stellarator concept is suitable for a fusion reactor. One of the most important issues for fusion reactors is the monitoring of plasma facing components when exposed to very high heat loads, through the use of visible and infrared (IR) cameras. In this paper, a new image processing system for the analysis of the strike lines on the inboard limiters from the first W7-X experimental campaign is presented. This system builds a model of the IR cameras through the use of spatial calibration techniques, helping to characterize the strike lines by using the information given by real spatial coordinates of each pixel. The characterization of the strike lines is made in terms of position, size, and shape, after projecting the camera image in a 2D grid which tries to preserve the curvilinear surface distances between points. The description of the strike-line shape is made by means of the Fourier Descriptors