Solid von Neumann algebras
Copyright policy )Solid von Neumann algebras
We prove that the relative commutant of a diffuse von Neumann subalgebra in a hyperbolic group von Neumann algebra is always injective. It follows that any non-injective subfactor in a hyperbolic group von Neumann algebra is non-Gamma and prime. The proof is based on C*-algebra theory.
6 pages. Minor Correction
- University of Tokyo Japan
hyperbolic group, Primary 46L10, General theory of von Neumann algebras, Mathematics - Operator Algebras, Secondary 20F67, FOS: Mathematics, Primary 46L10; Secondary 20F67, Operator Algebras (math.OA), solid von Neumann algebra, diffuse von Neumann algebra
hyperbolic group, Primary 46L10, General theory of von Neumann algebras, Mathematics - Operator Algebras, Secondary 20F67, FOS: Mathematics, Primary 46L10; Secondary 20F67, Operator Algebras (math.OA), solid von Neumann algebra, diffuse von Neumann algebra
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