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Lie theoretic significance of the measure topologies associated with a finite trace
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Daniel Beltiţă
Published/Copyright:
March 29, 2010
Abstract
Let ℳ be a W*-algebra with a faithful normal finite trace and think of the unitary group Uℳ endowed with the ultraweak topology. By using the measure topology associated with the aforementioned trace, we prove that Uℳ is a topological group with Lie algebra in the sense of K.H. Hofmann and S.A. Morris (J. Group Theory 8: 115–133, 2005). We discuss the corresponding exponential map and find that it is never locally injective in the case of factors of type II1.
Received: 2008-04-15
Accepted: 2008-05-27
Published Online: 2010-03-29
Published in Print: 2010-March
© de Gruyter 2010
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- Lp estimates for parabolic magnetic Schrödinger operators
- Calculation of UNil for the cyclic group of order two
- Lie theoretic significance of the measure topologies associated with a finite trace
- Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
- The finiteness of NK1(ℤ[G])
- Poincaré duality pairs of dimension three
- Optimal quantization of probabilities concentrated on small balls
- A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
- Homological localizations of Eilenberg–MacLane spectra
- A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
- The cohomology groups of the outer Whitehead automorphism group of a free product
- Dual topology of the motion groups
Articles in the same Issue
- Lp estimates for parabolic magnetic Schrödinger operators
- Calculation of UNil for the cyclic group of order two
- Lie theoretic significance of the measure topologies associated with a finite trace
- Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
- The finiteness of NK1(ℤ[G])
- Poincaré duality pairs of dimension three
- Optimal quantization of probabilities concentrated on small balls
- A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
- Homological localizations of Eilenberg–MacLane spectra
- A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
- The cohomology groups of the outer Whitehead automorphism group of a free product
- Dual topology of the motion groups
