Currents on Grassmann algebras

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 ${\mathbb{Z}}_2$-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.

20 pages, CPT-93/P.2935 and ENSLAPP-440/93

Cited by in corpus (5)

• Characteristic Cohomology and Observables in Higher Spin Gravity
• Higher Spin Gravities and Presymplectic AKSZ Models
• Supersymmetry and Noncommutative Geometry
• Berezin integration over anticommuting variables and cyclic cohomology
• Hochschild (co)homology of exterior algebras