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A brief review of abelian categorifications

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Mikhail Khovanov, Volodymyr Mazorchuk and Catharina Stroppel

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:
category, functor, abelian categorification,
braid group, Hecke algebra, Weyl algebra

2000 MSC:
18A22; 18A25; 16D90; 18E10; 18E15; 20C08

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 19, pp 479-508.

http://www.tac.mta.ca/tac/volumes/22/19/22-19.ps

http://www.tac.mta.ca/tac/volumes/22/19/22-19.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/19/22-19.ps

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/19/22-19.pdf

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