Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495781 | Journal of Functional Analysis | 2005 | 24 Pages |
Abstract
A Hilbert module over a planar algebra P is essentially a Hilbert module over a canonically defined algebra spanned by the annular tangles in P. It follows that any planar algebra Q containing P is a module over P, and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar algebra with the same modulus. We describe a positivity result that allows us to describe irreducible Temperley-Lieb planar algebra modules, and apply the result to decompose the planar algebras determined by the Coxeter graphs An (n⩾3), Dn (n⩾4), E6, E7, and E8.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Sarah A. Reznikoff,