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

Mohammed Guediri

Vol. 19 No. 2 (2014)

Regular Articles

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

Published 2014-09-15

Mohammed Guediri

Mohammed Guediri
King Saud University

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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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