The Fuglede-Kadison determinant, theme and variations

Details The Fuglede-Kadison determinant, theme and variations The Fuglede-Kadison determinant, theme and variations

2011-07-06

arxiv.org/abs/1107.1059v1

Mathematics

Operator Algebras

Scientific paper

We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison (1952), and a generalisation for appropriate groups of invertible elements in Banach algebras, from a paper by Skandalis and the author (1984). After some reminder on K-theory and Whitehead torsion, we hint at the relevance of these determinants to the study of $L^2$-torsion in topology.

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