A categorification of U_q sl(1,1) as an algebra
Quantum Algebra
2013-02-19 v2 Geometric Topology
Symplectic Geometry
Abstract
We construct families of differential graded algebras R and R \boxtimes R and give an algebraic formulation of the contact category of a disk through the differential graded category DGP(R) generated by some distinguished projective differential graded R-modules. The homology category H^0(DGP(R)) is a triangulated category and its Grothendieck group is a Clifford algebra. We then categorify the Clifford algebra to a functor from DGP(R \boxtimes R) to DGP(R). We construct a subcategory of the homology category which categorifies an integral version of U_q sl(1,1) as an algebra.
Keywords
Cite
@article{arxiv.1210.5680,
title = {A categorification of U_q sl(1,1) as an algebra},
author = {Yin Tian},
journal= {arXiv preprint arXiv:1210.5680},
year = {2013}
}
Comments
35 pages, 5 figures; added references