Tøkni, náttúra og náttúrutilfeing
Using graph C*-algebras to classify graph groupoids
Toke Meier Carlsen
Stuðul úr Granskingargrunninum:
Summary of project. Please note that if application is granted, the summary will be published on the Research Council’s website. (Complete description of the project is required and must be enclosed separately, max 10 pages – please consult Formal Requirements and Guidelines for applications) The project aims to use results and methods from the theory of C*-algebras to classify graph groupoids. This will be done by writing 3 papers. The first paper will look at which automorphisms of the K0 group of a graph C*-algebra that can be lifted to diagonal preserving *-isomorphisms of the graph C*-algebra. In the second paper, equivalence of graph groupoids will be studied, and in the third paper compact graph groupoids will be classified. The first paper will be written by the project manager and Professor Wojciech Szymanski from the University of Southern Denmark, and the other two papers by the project manager and Professor Søren Eilers from the University of Copenhagen. Together the 3 papers that will be written during the project will significantly contribute to the general theory of groupoids and increase our understanding of the interplay between groupoids and C*-algebras constructed from groupoids. In addition, the result described in the 3 papers are likely to have important applications to the theory of topological dynamical system, in particular symbolic dynamical systems, and will likely contribute to the further development of the classification of non-simple nuclear C*-algebras. It is also probable that these results will lead to interesting applications to the theory of Leavitt path algebras and the theory of Steinberg algebras. The 3 paper will be published in some of the world’s leading mathematical journals as open access papers.
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