Complete left-invariant affine structures on solvable non-unimodular three-dimensional Lie groups
Mohammed Guediri, Kholoud Al-Balawi
TL;DR
This paper classifies complete left-invariant affine structures on solvable non-unimodular three-dimensional Lie groups using an extension-based method rooted in left-symmetric algebra theory.
Contribution
It introduces a novel classification approach for affine structures on specific Lie groups through algebraic extensions.
Findings
Complete classifications obtained for the structures.
Identification of new affine structures on these Lie groups.
Method applicable to similar classification problems.
Abstract
In this paper, we shall use a method based on the theory of extensions of left-symmetric algebras to classify complete left-invariant affine real structures on solvable non-unimodular three-dimensional Lie groups.
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Taxonomy
TopicsAdvanced Topics in Algebra · Nonlinear Waves and Solitons · Advanced Algebra and Geometry