Tanaka structures modeled on extended Poincar\'e algebras

  title={Tanaka structures modeled on extended Poincar\'e algebras},
  author={Andrea Altomani and Andrea Santi},
  journal={arXiv: Differential Geometry},
  • Andrea Altomani, Andrea Santi
  • Published 2012
  • Mathematics, Physics
  • arXiv: Differential Geometry
  • Let (V,(.,.)) be a pseudo-Euclidean vector space and S an irreducible Cl(V)-module. An extended translation algebra is a graded Lie algebra m = m_{-2}+m_{-1} = V+S with bracket given by ([s,t],v) = b(v.s,t) for some nondegenerate so(V)-invariant reflexive bilinear form b on S. An extended Poincar\'e structure on a manifold M is a regular distribution D of depth 2 whose Levi form L_x: D_x\wedge D_x\rightarrow T_xM/D_x at any point x\in M is identifiable with the bracket [.,.]: S\wedge S… CONTINUE READING

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