Classification of complete left-invariant affine structures on the oscillator group
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 all complete left-invariant affine structures on the oscillator group.
Keywords
Left-invariant affine structures, left-symmetric algebras, extensions and cohomologies of Lie algebras and left-symmetric algebras.
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PDFISSN: 1331-0623 (Print), 1848-8013 (Online)