Models of CR manifolds and their symmetry algebras (Q6577787)

The paper under review is a nice survey article on recent results on symmetry algebras of CR manifolds that generalise classical work by Poincaré, Cartan, Tanaka, Chern, Moser and others. It is well known that most symmetric models of Levi non-degenerate CR manifolds are hermitian quadrics. The symmetries of such quadrics and their deformations are determined by their 2-jets. One of the generalisations surveyed in the article relates to CR manifolds of higher codimension. It was believed (based on a flawed result from the 1980s) that natural nondegeneracy conditions on the higher-codimensional quadrics also imply 2-jet determination of the symmetries. The article under review provides new results and examples that show that for any \(n\) there are quadrics with \(n\)-jet determination, but not \((n-1)\)-jet determination.\N\NOther generalisations concern Levi-degenerate models on finite and infinite multi-type.