Trace as an alternative decategorification functor
Abstract
Categorification is a process of lifting structures to a higher categorical level. The original structure can then be recovered by means of the so-called "decategorification" functor. Algebras are typically categorified to additive categories with additional structure and decategorification is usually given by the (split) Grothendieck group. In this expository article we study an alternative decategorification functor given by the trace or the zeroth Hochschild--Mitchell homology. We show that this form of decategorification endows any 2-representation of the categorified quantum sl(n) with an action of the current algebra U(sl(n)[t]) on its center.
Cite
@article{arxiv.1409.1198,
title = {Trace as an alternative decategorification functor},
author = {Anna Beliakova and Zaur Guliyev and Kazuo Habiro and Aaron D. Lauda},
journal= {arXiv preprint arXiv:1409.1198},
year = {2015}
}
Comments
47 pages with tikz figures. arXiv admin note: text overlap with arXiv:1405.5920 by other authors