Classification of complete left-invariant affine structures on the Oscillator group

2012/12/30 by Guediri, Mohammed
#53A15 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1212.6698

Abstract

The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method, we shall apply it to classify complete left-invariant affine structures on the oscillator group.

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