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Abelian subalgebras of von Neumann algebras from flat tori in locally symmetric spaces

Lookup NU author(s): Professor Guyan Robertson

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Abstract

Consider a compact locally symmetric space M of rank r, with fundamental group Γ. The von Neumann algebra VN (Γ) is the convolution algebra of functions f ∈ ℓ2(Γ) which act by left convolution on ℓ2(Γ). Let Tr be a totally geodesic flat torus of dimension r in M and let Γ0≅ ℤr be the image of the fundamental group of Tr in Γ. Then VN(Γ0) is a maximal abelian *-subalgebra of VN(Γ) and its unitary normalizer is as small as possible. If M has constant negative curvature then the Pukánszky invariant of VN (Γ0) is ∞. © 2005 Elsevier Inc. All rights reserved.

Publication metadata

Author(s): Robertson G

Publication type: Article

Publication status: Published

Journal: Journal of Functional Analysis

Year: 2006

Volume: 230

Issue: 2

Pages: 419-431

ISSN (print): 0022-1236

ISSN (electronic): 1096-0783

Publisher: Academic Press

URL: http://dx.doi.org/10.1016/j.jfa.2005.04.009

DOI: 10.1016/j.jfa.2005.04.009

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