Stroppel, C. (2005) Categorification of the {T}emperley-{L}ieb algebra, tangles and cobordisms via projective functors. Duke Mathematical Journal, 126(3), pp. 547-596. (doi: 10.1215/S0012-7094-04-12634-X)
Full text not currently available from Enlighten.
Abstract
To each generic tangle projection from the three-dimensional real vector space onto the plane, we associate a derived endofunctor on a graded parabolic version of the Bernstein-Gel'fand category $\mathcal{O}$. We show that this assignment is (up to shifts) invariant under tangle isotopies and Reidemeister moves and defines therefore invariants of tangles. The occurring functors are defined via so-called projective functors. The first part of the paper deals with the indecomposability of such functors and their connection with generalised Temperley-Lieb algebras which are known to have a realisation via decorated tangles. The second part of the paper describes a categorification of the Temperley-Lieb category and proves the main conjectures of [BFK]. Moreover, we describe a functor from the category of 2-cobordisms into a category of projective functors.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Stroppel, Dr Catharina |
| Authors: | Stroppel, C. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Duke Mathematical Journal |
| ISSN: | 0012-7094 |
| ISSN (Online): | 1547-7398 |
University Staff: Request a correction | Enlighten Editors: Update this record
Deposit and Record Details
Deposit and Record Details