Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra

ORAL

Abstract

We study the homology and cohomology groups of super Lie algebras of supersymmetries and of super Poincare Lie algebras in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. 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 Lie algebras.

*The work was partially supported by NSF grant DMS-0805989

Authors

  • Renjun Xu

    • Department of Physics, University of California, Davis

  • Albert Schwarz

    • Department of Mathematics, University of California, Davis

  • Michael Movshev

    • Department of Mathematics, Stony Brook University