# Hochshild's method for describing the Mackenzie obstruction for construction of transitive Lie algebroid

## TL;DR

This paper adapts Hochschild's cohomological methods for Lie algebra kernels to the context of transitive Lie algebroids, aiming to characterize the Mackenzie obstruction.

## Contribution

It extends Hochschild's framework to transitive Lie algebroids and establishes a corresponding theorem for the Mackenzie obstruction.

## Key findings

- Hochschild's techniques are applicable to transitive Lie algebroids.
- A new theorem describing the Mackenzie obstruction is proved.
- The approach bridges Lie algebra cohomology and Lie algebroid theory.

## Abstract

The technique developed in Hochschild's works "Lie algebra kernels and cohomology " and "Cohomology classes of finite dimensional kernels for Lie algebras " [2],[3] can be applied to the special case of transitive Lie algebroids. Our task is formulated to transfer the Hochschild construction to the case of transitive Lie algebroids and prove a similar theorem.