Supersymmetry algebra cohomology I: Definition and general structure
Friedemann Brandt
TL;DR
This paper introduces a cohomology framework for supersymmetry algebras, defining primitive elements using a BRST-type operator, and provides a systematic method for their computation across various dimensions.
Contribution
It defines supersymmetry algebra cohomology and primitive elements, and presents a systematic computational method applicable in diverse dimensions.
Findings
Defined supersymmetry algebra cohomology and primitive elements
Outlined a systematic computation method
Illustrated the method with simple examples
Abstract
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.
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