A categorification of U_q sl(1,1) as an algebra

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.