Non occurrence of star graphs as principal graphs

Said A. Rida
Additional contact information
Said A. Rida: The University of New South Wales, School of Mathematics

A chapter in Algebraic Methods in Operator Theory, 1994, pp 205-217 from Springer

Abstract: Abstract Let N ⊂ M be an irreducible, finite depth, finite index inclusion of hyperfinite II 1-factors. The question of which graphs occur as principal graphs has been settled by various authors when the index is ≤ 4 and is still open for the remaining values. In an unpublished work, Haagerup proved that the smallest irreducible, finite depth subfactor of the hyperfinite II 1-factor with index above 4 has index (5+√13)/2 and principal graph T(4,4,4) (cf. def 1.3). Independantly from Haagerup’s result, we use the gaps in Popa’s set Γ(M, N) (cf. [4]) to prove that star graphs do not occur as principal graphs when the index is in (4, 2+√5).

Keywords: Finite Index; Finite Depth; Star Graph; White Vertex; Finite Dimensional Algebra (search for similar items in EconPapers)
Date: 1994
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0255-4_21

Ordering information: This item can be ordered from
http://www.springer.com/9781461202554

DOI: 10.1007/978-1-4612-0255-4_21

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().