Einstein manifolds and extended Poincar\'{e} algebras

Abstract

For any pseudo-Euclidean space $V \simeq \mathbb{R}^{p, q}, p \geq 3$ and module $W$ over the even Clifford algebra $\text{Cl}^{0}(V)$, V. C\'{o}rtes 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 $V\simeq \mathbb{R}^{p, q}, p\equiv 3 \pmod{4}$ and an irreducible $\text{Cl}^{0}(V)$-module $W$.