Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
M.V. Movshev, A. Schwarz, Renjun Xu
TL;DR
This paper analyzes the homology and cohomology of super Lie algebras related to supersymmetries and super Poincare algebra across multiple dimensions, providing comprehensive results for dimensions up to 11.
Contribution
It offers complete homology and cohomology classifications for non-extended supersymmetry in all dimensions up to 11, including reductions in 10 and 11 dimensions.
Findings
Complete homology and cohomology results for supersymmetry in dimensions ≤11
Descriptions of reduced supersymmetry algebra cohomology in 10 and 11 dimensions
Method applicability to extended supersymmetry algebra
Abstract
We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions . For dimensions we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry algebra.
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