# Extension of Malcev algebra and applications to gravity

## TL;DR

This paper explores extensions of Malcev algebras, introduces a new algebraic identity, and connects these mathematical structures to applications in general relativity.

## Contribution

It provides explicit examples of extended Malcev algebras and a new algebraic identity generalizing known identities, linking algebraic structures to gravity.

## Key findings

- Extended Malcev algebras constructed
- New algebraic identity introduced
- Connection established with general relativity

## Abstract

We investigate extensions of Malcev algebras and give an explicit example of extended algebras. We present a new algebraic identity, which can be regarded as a generalization of the Jacobi identity or the Malcev identity. As applications to gravity, we demonstrate that the extended algebra can be linked with general relativity.