Central Extension of Left Alternative Algebras and the Second Cohomology Group

Abstract

The purpose of this paper is to prove that the second cohomology group $H^2\left(A,\mathbb{F}\right)$ of a left alternative algebra $A$ over an algebraically closed field $\mathbb{F}$ of characteristic 0 can be interpreted as the set of equivalent classes of one-dimensional central extensions of $A$ .