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Register a new userTanaka structures modeled on extended Poincare algebras
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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 Poincare structure on a manifold M is a regular distribution D of depth 2 whose Levi form L_x: D_xwedge D_xrightarrow T_xM/D_x at any point xin M is identifiable with the bracket [.,.]: Swedge Srightarrow V of a fixed extended translation algebra m. The classification of the standard maximally homogeneous manifolds with an extended Poincare structure is given, in terms of Tanaka prolongations of extended translation algebras and of appropriate gradations of real simple Lie algebras.
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