  The paper concerns standard supersymmetry algebras in diverse dimensions,
involving bosonic translational generators and fermionic supersymmetry
generators. A cohomology related to these supersymmetry algebras, termed
supersymmetry algebra cohomology, and corresponding "primitive elements" are
defined by means of a BRST-type coboundary operator. A method to systematically
compute this cohomology is outlined and illustrated by simple examples.
