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 Z 2-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.
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