Tanaka structures modeled on extended Poincaré algebras Andrea AltomaniAndrea Santi 53C3058A3053C2753C80Tanaka prolongationsextended Poincare algebrasextended translation algebrasClifford algebras and spinors Let $(V,(\cdot,\cdot))$ be a pseudo-Euclidean vector space and $S$ an irreducible $C\ell(V)$-module. An extended translation algebra is a graded Lie algebra $\mathfrak{m}=\mathfrak{m}_{-2}+\mathfrak{m}_{-1}=V+S$ with bracket given by $([s,t],v)=b(v\cdot s,t)$ for some nondegenerate $\mathfrak{so}(V)$-invariant reflexive bilinear form $b$ on $S$. An extended Poincar\'e structure on a manifold $M$ is a regular distribution $\mathcal{D}$ of depth $2$ whose Levi form $\mathcal{L}_x:\mathcal{D}_x\wedge\mathcal{D}_x\to T_x M/\mathcal{D}_x$ at any point $x\in M$ is identifiable with the bracket $[\cdot,\cdot]\colon S\wedge S\to V$ of a fixed extended translation algebra $\mathfrak{m}$. The classification of the standard maximally homogeneous manifolds with an extended Poincar\'e structure is given, in terms of Tanaka prolongations of extended translation algebras and of appropriate gradations of real simple Lie algebras. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5186 10.1512/iumj.2014.63.5186 en Indiana Univ. Math. J. 63 (2014) 91 - 117 state-of-the-art mathematics http://iumj.org/access/