Einstein manifolds and extended Poincaré algebras

Abstract

For any pseudo-Euclidean space $V\simeq {\mathbb{R}}^{p,q},p\ge 3$ and module $W$ over the even Clifford algebra ${\text{Cl}}^0(V)$, V. Córtes constructed noncompact homogeneous quaternion pseudo-Kahler space. In particular, such homogeneous space is always Einstein and for $p=3$ it is Riemannian. Based on this approach we construct the series of Riemannian Einstein homogoneous spaces with negative scalar curvature associated with $V\simeq {\mathbb{R}}^{p,q},p\equiv 3(\mathrm{mod}4)$ and an irreducible ${\text{Cl}}^0(V)$-module $W$.