(The) classification of three dimensional pseudo-riemannian algebras with absolute left zero divisor

Abstract

The primary concern in this paper is to investigate invariant pseudo-Riemannian connections on G/H in terms of its associated algebras defined on the tangent space $T(G/H,\bar{e})$ at $\bar{e} = eH$. We classify the three dimensional pseudo-Riemannian algebras with absolute left zero divisor and three dimensional nonsimple Riemannian algebras.