Leibniz algebras constructed by Witt algebras

TL;DR

This paper explores the construction of infinite-dimensional Leibniz algebras linked to the Witt algebra and investigates their cohomological properties, revealing triviality in low-dimensional cohomology groups.

Contribution

It introduces a method to construct Leibniz algebras from Witt algebras and proves the triviality of certain cohomology groups, advancing understanding of their algebraic structure.

Findings

Infinite-dimensional Leibniz algebras associated with the Witt algebra are described.

Low-dimensional Leibniz cohomology groups of the Witt algebra are shown to be trivial.

Provides new insights into the cohomological properties of these algebras.

Abstract

We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself.