Irreducible holonomy algebras of Riemannian supermanifolds

Abstract

Possible irreducible holonomy algebras $\g\subset\osp(p,q|2m)$ of Riemannian supermanifolds under the assumption that $\g$ is a direct sum of simple Lie superalgebras of classical type and possibly of a one-dimensional center are classified. This generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian manifolds.

arXiv comment27 pages, the final version

References in corpus (5)

• One component of the curvature tensor of a Lorentzian manifold
• Holonomy of supermanifolds
• Irreducible complex skew-Berger algebras
• Fedosov and Riemannian supermanifolds
• On Local Calabi-Yau Supermanifolds and Their Mirrors

Cited by in corpus (4)

• Riemannian structures on ${\mathbb{Z}}_2^n$-manifolds
• Symplectic ${\mathbb{Z}}_2^n$-manifolds
• Modular Classes of Q-Manifolds, Part II: Riemannian Structures & Odd Killing Vectors Fields
• The super-Sasaki metric on the antitangent bundle