Homology of Lie algebra of supersymmetries and of super Poincare Lie 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 $\le 11$. For dimensions $D=10,11$ we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry algebra.

arXiv commentNew version with some additions and corrections

References in corpus (6)

• Symmetry Principles in Quantum Systems Theory
• GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions
• The cohomology of superspace, pure spinors and invariant integrals
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Cited by in corpus (16)

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• Perspectives on the pure spinor superfield formalism
• M-theory from the Superpoint
• Supersymmetry algebra cohomology IV: Primitive elements in all dimensions from D=4 to D=11
• Superspace de Rham Complex and Relative Cohomology
• The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity
• SUSY Invariants from the BRST Cohomology of the SOSO Model
• An Extraordinary Mass Invariant and an Obstruction in a Massive Superspin One Half Model made with a Chiral Dotted Spinor Superfield
• BRST cohomology of the sum of two pure spinors
• Cohomology ring of the BRST operator associated to the sum of two pure spinors
• The Derived Pure Spinor Formalism as an Equivalence of Categories
• Integral invariants in flat superspace
• Six-dimensional supermultiplets from bundles on projective spaces