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ISSN 1088-9485(e) ISSN 0273-0979(p)

A splitting property for subalgebras of tensor products

Author(s): Liming Ge
Journal: Bull. Amer. Math. Soc. 32 (1995), 57-60.
MathSciNet review: 1273397
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Abstract | References | Additional information

Abstract: We prove a basic result about tensor products of a ${\text{I}}{{\text{I}}_1}$ factor with a finite von Neumann algebra and use it to answer, affirmatively, a question asked by S. Popa about maximal injective factors.

References:

Bibliography

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[M-vN]: F. Murray and J. von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), 116-229. MR 1503275
[P1]: S. Popa, Maximal injective subalgebras in factors associated with free groups, Adv. Math. 50 (1983), 27-48. MR 720738 (85h:46084)
[P2]: -, On a problem of R. V. Kadison on maximal abelian *-subalgebras in factors, Invent. Math. 65 (1981), 269-281. MR 641131 (83g:46056)
[Sc]: J. Schwartz, Two finite, non-hyperfinite, non-isomorphic factors, Comm. Pure Appl. Math. 16 (1963), 19-26. MR 0149322 (26:6812)
[To]: J. Tomiyama, Tensor products and projections of norm one in von Neumann algebras, Seminar notes, Math. Institute, University of Copenhagen, 1970.

Additional Information:

DOI: 10.1090/S0273-0979-1995-00556-2
PII: S 0273-0979(1995)00556-2
Keywords: von Neumann algebras, injective factors, slice maps, tensor products
Copyright of article: Copyright 1995, American Mathematical Society

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