# Finitness of prolongations of graded Lie algebras

@article{Marini2018FinitnessOP, title={Finitness of prolongations of graded Lie algebras}, author={Stefano Marini and Costantino Medori and Mauro Nacinovich}, journal={arXiv: Differential Geometry}, year={2018} }

We find necessary and sufficient conditions for the finiteness of Tanaka's maximal prolongation of fundamental graded Lie algebras. In the final part we discuss some examples of simple prolongations.

## One Citation

LISTA DELLE PUBBLICAZIONI

- Mathematics
- 2019

[1] Mauro Nacinovich. Monotone operators of finite degree. Boll. Un. Mat. Ital. (4), 6:134–139, 1972. [2] Mauro Nacinovich. Una osservazione su una congettura di De Giorgi. Boll. Un. Mat. Ital. (4),…

## References

SHOWING 1-10 OF 25 REFERENCES

On transitive contact and CR algebras

- MathematicsANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- 2020

We consider locally homogeneous $CR$ manifolds and show that, under a condition only depending on their underlying contact structure, their $CR$ automorphisms form a finite dimensional Lie group.

Primitive subalgebras of exceptional Lie algebras

- Mathematics
- 1971

The object of this paper is to classify (up to inner automorphism) the primitive, maximal rank, reductive subalgebras of the (complex) exceptional Lie algebras. By primitive we mean that the…

Semi-Simple Lie Algebras and Their Representations

- Mathematics
- 1984

This paper presents an overview of the representations of Lie algebras, particularly semi-simple Lie algebras, with a view towards theoretical physics. We proceed from the relationship between Lie…

Infinite dimensional primitive Lie algebras

- Mathematics
- 1970

Transitivity questions in differential geometry can often be reduced to problems involving a certain type of "topologized" Lie algebra. In [6] we developed a structure theory for such algebras…

Prolongation of Tanaka structures: an alternative approach

- Mathematics
- 2016

The classical theory of prolongation of G-structures was generalized by N. Tanaka to a wide class of geometric structures (Tanaka structures), which are defined on a non-holonomic distribution.…

Irreducible Lie algebras of infinite type

- Mathematics
- 1971

Let F be a finite dimensional vector space over an algebraically closed field of characteristic^2, 3, 5. It is shown that if LCZg\(V) is an irreducible Lie algebra of infinite type then either…

Idéaux fermés de fonctions différentiables

- 1972

Ce chapitre contient deux resultats essentiels: d’une part, le classique theoreme spectral de Whitney; d’autre part, le theoreme 5.6. Ce dernier jouera un role essentiel au chapitre VI et dans la…

The remarkable algebra so*(2n), its representations, its Clifford algebra and potential applications

- Mathematics
- 1990

Properties of the real Lie algebra so*(2n) and its finite-dimensional representations are described. The structure of the Clifford algebras associated with the two fundamental spinor representations…

Lectures on Differential Geometry

- Mathematics
- 1964

Algebraic Preliminaries: 1. Tensor products of vector spaces 2. The tensor algebra of a vector space 3. The contravariant and symmetric algebras 4. Exterior algebra 5. Exterior equations…