Tanaka structures modeled on extended Poincar\'e algebras
| Autor: | Altomani, Andrea, Santi, Andrea |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Indiana University Mathematics Journal 63 issue 1 (2014), 91-117 |
| Druh dokumentu: | Working Paper |
| Popis: | 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\rightarrow V of a fixed extended translation algebra 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. Comment: 23 pages, 4 tables v2: minor revision v3: Major revision of the introduction |
| Databáze: | arXiv |
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