The exterior graded Swiss-Cheese Operad ?VS2

In this paper we introduce (A)(S)2(V) a generalization of the exterior algebra of a vector space V. We study some of its properties and give explicit computations for the case dim(V-2) = 2. In particular we show the existence and uniqueness of a determinant-like function (det)(S)2 : V- 2(circle times 6) -> k with the property that detS2(circle times(1 )<= i < j <= 4(vi,j))=0ifthereexists1 <= x < y < z <= 4 such thatvx,y=vx,z=vy,z. We also introduce the notion of GSC-operads and showhow lambda(2)(S)Vfits in that context.