TY - JOUR

T1 - Examples of prime von neumann algebras

AU - Gao, Mingchu

AU - Junge, Marius

PY - 2007

Y1 - 2007

N2 - Let {(Mi, Pdbli) : i = 1, 2, . . .} be a family of injective von Neumann algebras on separable Hilbert spaces with a faithful normal state fi on each Mi and M be the reduced free product von Neumann algebra of (Mi, Pdbli), iε N. If there is a normal conditional expectation from M onto a non-injective von Neumann subalgebra N of M, then N is prime, i.e., N = N1⊗̄N2 implies that either N1 or N2 is a von Neumann algebra of type I. This result provides many examples of prime von Neumann algebras. These examples of prime von Neumann algebras include prime factors given by Ge (type II1) and by Shlyakhtenko (Type III). In our proof we combine Ozawa's new techniques for solid von Neumann algebras with Shlyakhtenko's "matrix model" techniques for the free Araki- Woods factors.

AB - Let {(Mi, Pdbli) : i = 1, 2, . . .} be a family of injective von Neumann algebras on separable Hilbert spaces with a faithful normal state fi on each Mi and M be the reduced free product von Neumann algebra of (Mi, Pdbli), iε N. If there is a normal conditional expectation from M onto a non-injective von Neumann subalgebra N of M, then N is prime, i.e., N = N1⊗̄N2 implies that either N1 or N2 is a von Neumann algebra of type I. This result provides many examples of prime von Neumann algebras. These examples of prime von Neumann algebras include prime factors given by Ge (type II1) and by Shlyakhtenko (Type III). In our proof we combine Ozawa's new techniques for solid von Neumann algebras with Shlyakhtenko's "matrix model" techniques for the free Araki- Woods factors.

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U2 - 10.1093/imrn/rnm042

DO - 10.1093/imrn/rnm042

M3 - Article

AN - SCOPUS:77955570267

SN - 1073-7928

VL - 2007

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

M1 - rnm042

ER -