A brief review of abelian categorifications
Representation Theory
2007-05-23 v2 Category Theory
Abstract
This article contains a review of categorifications of semisimple representations of various rings via abelian categories and exact endofunctors on them. A simple definition of an abelian categorification is presented and illustrated with several examples, including categorifications of various representations of the symmetric group and its Hecke algebra via highest weight categories of modules over the Lie algebra sl(n). The review is intended to give non-experts in representation theory who are familiar with the topological aspects of categorification (lifting quantum link invariants to homology theories) an idea for the sort of categories that appear when link homology is extended to tangles.
Keywords
Cite
@article{arxiv.math/0702746,
title = {A brief review of abelian categorifications},
author = {Mikhail Khovanov and Volodymyr Mazorchuk and Catharina Stroppel},
journal= {arXiv preprint arXiv:math/0702746},
year = {2007}
}
Comments
latex, 35 pages, 4 eps figures