A categorification of U-T (Sl(1/1)) and its tensor product representations

作者：Tian Yin^*

来源：Geometry and Topology, 2014, 18(3): 1635-1717.

We define the Hopf superalgebra U-T (sl(1/10), which is a variant of the quantum supergroup U-q (sl (1/1) and its representations V-1(circle times n) for n > 0. We construct families of DG algebras A, B and R n, and consider the DG categories DGP(A), DGP(B) and DGP (R-n) which are full DG subcategories of the categories of DG A-, B- and R-n-modules generated by certain distinguished projective modules. Their 0th homology categories IIP(A), IIP(B) and IIP (R-n) are triangulated and give algebraic formulations of the contact categories of an annulus, a twice punctured disk and an n times punctured disk. Their Grothendieck groups are isomorphic to UT (sl(1/1) U Tsl 1ZUTsl1and Vn1, respectively. We categorify the multiplication and comultiplication on UTsl1j1 to a bifunctor HPA HP HP A and a functor HP A HP respectively. The UTsl j1-action on Vn1is lifted to a bifunctor HPAHP RnHP Rn

• 出版日期2014