Singular subfactors of II₁ factors /
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis eBook |
| Language: | English |
| Published: |
[College Station, Tex.] :
[Texas A&M University],
[2007]
|
| Subjects: | |
| Online Access: | Link to OAK Trust copy |
| Abstract: | We examine the notion of a-strong singularity for subfactors N of a II₁ factor M, which is a metric quantity that relates the distance of a unitary to a subalgebra with the distance between that subalgebra and its unitary conjugate. Using work of Popa, Sinclair, and Smith, we show that there exists an absolute constant 0 < c < 1 such that all singular subfactors are c-strongly singular. Under the hypothesis that N' h[M, eN] is 2-dimensional, we prove that finite index subfactors are 1-strongly singular with a constant that tends to 1 as the Jones Index tends to infinity and infinite index subfactors are 1-strongly singular. We provide examples of subfactors satisfying these conditions using group theoretic constructions. Specifically, if P is a II₁ factor and G is a countable discrete group acting on P by outer automorphisms, we characterize the elements x of PoG such that x(PoH)x0 PoH for some subgroup H of G. We establish that proper finite index singular subfactors do not have the weak asymptotic homomorphism property, in contrast to the case for masas. In the infinite index setting, we discuss the role of the semigroup of one-sided normalizers with regards to the question of whether all infinite index singular subfactors have the weak asymptotic homomorphism property. Finally, we provide a characterization of singularity for finite index subfactors in terms of the traces of projections in N' [M, eN] and use this result to show that fixed point subfactors of outer Zp for p prime are regular. The characterization extends to infinite index subfactors by replacing singular with contains its one-sided normalizers. |
|---|---|
| Item Description: | "Major Subject: Mathematics" Title from author supplied metadata (automated record created on Nov. 2, 2007.) Vita. Abstract. Electronic resource. |
| Format: | Mode of access: World Wide Web. System requirements: World Wide Web access and Adobe Acrobat Reader. |
| Bibliography: | Includes bibliographical references. |