On contact and finitely Levi-nondegenerate CR algebras

We study CR-manifolds of arbitrary CR codimension, mainly focusing on Levi and contact-nondegeneracy and depth. We investigate these and other invariants in the locally homogeneous case, developing a comprehensive theory which establishes correspondences with related properties of the associated CR-algebras and, in the parabolic case, with the combinatorics of their cross-marked painted root diagrams.