Abelian subalgebras of von Neumann algebras from flat tori in locally symmetric spaces
| Autor: | Guyan Robertson |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Fundamental group Mathematics::Operator Algebras Astrophysics::High Energy Astrophysical Phenomena Mathematical analysis Subalgebra Mathematics - Operator Algebras Group algebra Centralizer and normalizer von Neumann algebra symbols.namesake Differential Geometry (math.DG) Von Neumann algebra Symmetric space Locally symmetric space FOS: Mathematics symbols Abelian von Neumann algebra Abelian group Operator Algebras (math.OA) 22D25 22E40 Masa Analysis Mathematics |
| Zdroj: | Journal of Functional Analysis. 230:419-431 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2005.04.009 |
| Popis: | 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 ∈ l 2 ( Γ ) which act by left convolution on l 2 ( Γ ) . Let T r be a totally geodesic flat torus of dimension r in M and let Γ 0 ≅ Z r be the image of the fundamental group of T r in Γ . Then VN ( Γ 0 ) 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 Pukanszky invariant of VN ( Γ 0 ) is ∞ . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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