The Laplacian subalgebra of $\mathcal {L}(\mathbb {F}_N)^{\overline {\otimes }_k}$ is a strongly singular masa
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- by Teodor Ştefan Bîldea PDF
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Abstract:
In this paper, we present a new class of strongly singular maximal abelian subalgebras living inside the $k$-folded tensor product of the free group factor $\mathcal {L}(\mathbb {F}_N)$ with itself ($N\ge 2$). The notions of strongly singular masas in type $\mathrm {II}_1$ factors and that of asymptotic homomorphism were introduced by A. Sinclair and R. Smith. One of their first examples was the Laplacian subalgebra of the free group factor, generated by the sum of words of length 1 in $\mathbb {F}_N$. This subalgebra was known to be a singular masa. Using the results of A. Sinclair and R. Smith, we show that the unique trace-preserving conditional expectation onto the Laplacian subalgebra of $\mathcal {L}(\mathbb {F}_N)^{\overline {\otimes }_k}$ is an asymptotic homomorphism, and hence the Laplacian subalgebra is a strongly singular masa for every $k\ge 1$.References
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Additional Information
- Teodor Ştefan Bîldea
- Affiliation: Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242
- Address at time of publication: Computational Biomedicine Lab, Texas Learning and Computation Center, University of Houston, 4800 Calhoun Road, Room 218 Philip Guthrie Hoffman Hall (PGH), Houston, Texas 77204
- Email: teodor.bildea@mail.uh.edu
- Received by editor(s): March 23, 2005
- Received by editor(s) in revised form: October 17, 2005
- Published electronically: August 31, 2006
- Communicated by: Joseph A. Ball
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 823-831
- MSC (2000): Primary 46L10; Secondary 20E05
- DOI: https://doi.org/10.1090/S0002-9939-06-08548-0
- MathSciNet review: 2262878