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The local index formula in semifinite von Neumann algebras II: The even case |
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| Authors: | Alan L Carey Adam Rennie |
| Institution: | a Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia b Department of Mathematics and Statistics, University of Victoria, Room D227, Clearihue Building, 3800 Finnerty Road (Ring Road), Victoria, BC, Canada V8W 3P4 c School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia d School of Informatics and Engineering, Flinders University, Bedford Park, SA 5042, Australia |
| Abstract: | We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I. To allow for algebras with a non-trivial centre we have to establish a theory of unbounded Fredholm operators in a general semifinite von Neumann algebra and in particular prove a generalised McKean-Singer formula. |
| Keywords: | primary 19K56 46L80 secondary 58B30 46L87 |
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