# On conformal pseudo-subriemannian fundamental graded Lie algebras associated with pseudo $H$-type Lie algebras

## TL;DR

This paper explores the structure and prolongations of conformal pseudo-subriemannian fundamental graded Lie algebras derived from pseudo H-type Lie algebras, revealing conditions under which their prolongations coincide.

## Contribution

It establishes the equivalence of prolongations for these Lie algebras under specific assumptions, advancing understanding of their structural properties.

## Key findings

- Prolongation of conformal pseudo-subriemannian graded Lie algebra matches that of the fundamental graded Lie algebra under certain conditions.
- Provides new insights into the structure of pseudo H-type Lie algebras and their associated graded Lie algebras.
- Enhances the theoretical framework connecting conformal structures and graded Lie algebra prolongations.

## Abstract

A pseudo $H$-type Lie algebra naturally gives rise to a conformal pseudo-subriemannian fundamental graded Lie algebras. In this paper we investigate the prolongations of the associated fundamental graded Lie algebra and the associated conformal pseudo-subriemannian fundamental graded Lie algebra. In particular, we show that the prolongation of the associated conformal pseudo-subriemannian fundamental graded Lie algebra coincides with that of the associated fundamental graded Lie algebra under some assumptions.