Fuglede-Kadison determinant: theme and variations

作者：de la Harpe Pierre^*

来源：Proceedings of the National Academy of Sciences of the United States of America, 2013, 110(40): 15864-15877.

DOI：10.1073/pnas.1202059110

We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison [Fuglede B, Kadison R (1952) Ann Math 55: 520-530], and a generalization for appropriate groups of invertible elements in Banach algebras, from a paper by Skandalis and the author (1984). After some discussion of K-theory and Whitehead torsion, we indicate the relevance of these determinants to the study of L-2-torsion in topology. Contents are as follows:
1. The classical setting.
2. On von Neumann algebras and traces.
3. Fuglede-Kadison determinant for finite von Neumann algebras.
4. Motivating question.
5. Brief reminder of K-0, K-1, K-1(top), and Bott periodicity.
6. Revisiting the Fuglede-Kadison and other determinants.
7. On Whitehead torsion.
8. A few lines on L-2-torsion.

• 出版日期2013-10-1