Classifiability of crossed products by csc nilpotent Lie groups

Sven Raum  (Institut f¨¹r Mathematik Universit?t Potsdam)

13:30-14:30£¬July 30£¬2024    Tian Jiabing Building 323


Driven by the success of Elliott's classification programme for amenable C*-algebras, there has been interest in understanding which topological dynamical systems give rise to classifiable C*-algebras via the crossed product construction. Regularity, e.g. in the incarnation of finite nuclear dimension of the crossed product C*-algebra, is typically the hardest aspect to understand. Adressing this problem for connected groups for the first time, work of Hirshberg-Szabo-Winter-Wu from 2017 showed that crossed products by free actions of the real numbers have nuclear dimension controlled by the covering dimension of the space acted on. Later, Hirschberg-Wu could generalise this result, dropping the freeness assumption. I will report on joint work with Ulrik Enstad and Gabriel Favre extending the nuclear dimension bounds of Hirschberg-Szabo-Winter-Wu to free actions of connected simpliy connected nilpotent Lie groups. Prior to this work, no larger classes of Lie groups than the real numbers could be dealt with.

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