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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...
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