Finite-dimensionality in Tanaka theory

Abstract

In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.

In this version I extend the last section by including a description of all rank 2 and 3 distributions with infinite-dimensional symmetry algebra. The second proof of Theorem 1 for semi-strongly regular case is omitted in this version (as excessive), but it is valid/accessible through version 1.

References in corpus (4)

• On Tanaka's Prolongation Procedure for Filtered Structures of Constant Type
• On automorphism groups of some types of generic distributions
• Graded nilpotent Lie algebras of infinite type
• Rank 2 distributions of Monge equations: symmetries, equivalences, extensions

Cited by in corpus (8)

• The gap phenomenon in parabolic geometries
• Symmetries of filtered structures via the filtered Lie equations
• Jet-determination of symmetries of parabolic geometries
• On local geometry of vector distributions with given Jacobi symbols
• Lowest degree invariant 2nd order PDEs over rational homogeneous contact manifolds
• The gap phenomenon in the dimension study of finite type systems
• L-prolongations of graded Lie algebras
• On 3-nondegenerate CR manifolds in dimension 7 (II): the intransitive case