Homogeneous real \((2,3,5)\) distributions with isotropy (Q2633021)

\textit{E. Cartan} [Ann. Sci. Éc. Norm. Supér. (3) 27, 109--192 (1910; JFM 41.0417.01)] initiated the study of \((2, 3, 5)\) distributions, that is, tangent 2-plane distributions (\(M, D)\) on 5-manifolds satisfying the genericity condition \([D, [D, D]]= TM\). In the article under review. the author classifies locally all homogeneous real \((2, 3, 5)\) distributions with multiply transitive symmetry algebra, for which \(\dim \mathfrak{aut} (D) \ge 6\). The methods are standard. Any homogenous \((2, 3, 5)\) distribution (\(M, D)\) can be encoded in an algebraic model. For each distribution in the classification an explicit algebraic model in terms of abstract Lie algebra data is given. Most of these distributions were identified by Cartan [loc. cit.]. Algorithms for identifying, in both the complex and real cases, a multiply transitive homogeneous \((2, 3, 5)\) distribution given in terms of an abstract algebraic model among the distributions in the classification are presented. This amounts to constructing sufficiently many invariants to distinguish all of the models.