2013/04/09 by Lionel Bérard Bergery, Bergery, Lionel Bérard
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1304.2622
openalex publication_date 2013/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
That announcement gives the structure of totally reducible linear Lie algebras which are the Lie algebra of the holonomy group of (at least) one torsion-free connection. The result uses the (already known) classi cation of the irreducible ones and some previous (unpublished) works by the author giving the classi cation for the pseudo-riemannian totally reducible case. One describes those Lie subalgebras through a general structure theorem involving two constructions and some lists. These constructions give new examples of non irreducible totally reducible holonomy algebras and also recover some irreducible ones which seem missing in the previous classi cation.