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Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents
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Christopher Deninger
Published/Copyright:
December 20, 2010
Abstract
For an ergodic measure preserving action on a probability space, consider the corresponding crossed product von Neumann algebra. We calculate the Fuglede–Kadison determinant for a class of operators in this von Neumann algebra in terms of the Ljapunov exponents of an associated measurable cocycle. The proof is based on recent work of Dykema and Schultz. As an application one obtains formulas for the Fuglede–Kadison determinant of noncommutative polynomials in the von Neumann algebra of the discrete Heisenberg group. These had been previously obtained by Lind and Schmidt via entropy considerations.
Received: 2008-10-08
Revised: 2009-09-01
Published Online: 2010-12-20
Published in Print: 2011-February
© Walter de Gruyter Berlin · New York 2011
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Articles in the same Issue
- On the theta series of p-th order
- Deformations of canonical pairs and Fano varieties
- Subnormal solutions of non-homogeneous periodic ODEs, special functions and related polynomials
- Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents
- The cohomology of locally analytic representations
Articles in the same Issue
- On the theta series of p-th order
- Deformations of canonical pairs and Fano varieties
- Subnormal solutions of non-homogeneous periodic ODEs, special functions and related polynomials
- Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents
- The cohomology of locally analytic representations
