Journal of Geometry and Physics 15 (1995) 333-352
Abstract : We define currents on a Grassmann algebra Gr(N) with N generators as distributions on its exterior algebra (using the symmetric wedge product). We interpret the currents in terms of -graded Hochschild cohomology and closed currents in terms of cyclic cocycles (they are particular multilinear forms on Gr(N)). An explicit construction of the vector space of closed currents of degree p on Gr(N) is given by using Berezin integration.
Grassmann algebras, super-algebras, supersymmetries, supermanifolds, Hochschild and cyclic cohomologies, De Rham currents.
CPT - 93 / P.2935
ENSLAPP - 440/93