Játtað í: 2019 Granskingarøki: Tøkni, náttúra og náttúrutilfeing Verkætlanarslag: Verkætlan Verkætlanarheiti: Using graph C*-algebras to classify graph groupoids Játtanarnummar: 0457 Verkætlanarleiðari: Toke Meier Carlsen Stovnur/virki: Náttúruvísindadeildin Verkætlanarskeið: Original: 01/07/2019-30/06/2020 Final: 01/07/2019-31/01/2022 Samlaður kostnaður: 395.319 Stuðul úr Granskingargrunninum: 105.000 Verkætlanarlýsing: Original 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. Final The aim of the project was to use results and methods from the theory of C*-algebras to classify graph groupoids. The outcome of the project is the 4 papers mentioned below. Three of this are finished and have been submitted for publication, while the forth is expected to be finished and submitted for publication later this year. In the four papers graph groupoids (and also more general classes of groupoids) are classified up to different kinds of equivalence with the help of C*-algebras. Støða: Liðug Avrik: Scientific articles, books, thesis etc. 1. Kevin Aguyar Brix and Toke Meier Carlsen: “C*-algebras, groupoids and covers of shift spaces”, Trans. Amer. Math. Soc. Ser. B 7 (2020), 134-185. doi:10.1090/btran/53. 2. Toke Meier Carlsen, Adam Dor-On and Søren Eilers: “Shift equivalence through the lens of Cuntz-Krieger algebras”, arXiv:2011.10320, 20 pages. 3. Becky Armstrong, Kevin Aguyar Brix, Toke Meier Carlsen and Søren Eilers: “Conjugacy of local homeomorphisms via groupoids and C*-algebras”, arXiv:2105.00479, 19 pages. Other results, such as unpublished articles, patents, computer systems, original models and new procedures 1. Becky Armstrong, Kevin Aguyar Brix, Toke Meier Carlsen and Søren Eilers: “An algorithm for deciding conjugacy of graphs”, in preparation. << Back |
Administration English |