Reconstruction from Representations: Jacobi via Cohomology

Abstract

A subalgebra of a Lie algebra $\mathfrak{h}\subset \mathfrak{g}$ determines $\mathfrak{h}$-representation $\rho$ on $\mathfrak{m}=\mathfrak{g}/\mathfrak{h}$. In this note we discuss how to reconstruct $\mathfrak{g}$ from $(\mathfrak{h},\mathfrak{m},\rho )$. In other words, we find all the ingredients for building non-reductive Klein geometries. The Lie algebra cohomology plays a decisive role here.

v2: typo in the definition of q_sigma on p.3 is corrected; reference [9] updated

References in corpus (1)

• Non-degenerate Para-Complex Structures in 6D with Large Symmetry Groups

Cited by in corpus (2)

• Non-degenerate Para-Complex Structures in 6D with Large Symmetry Groups
• Erratum to: Almost complex structures in 6D with non-degenerate Nijenhuis tensors and large symmetry groups