Asian-European Journal of Mathematics · 2009 · 12 citations · 3 references
Natural SciencesMathematicsAlgebraGeometrySet TheoryAbstract AlgebraAlgebraic GeometryGroup TheoryHomological AlgebraLie AlgebrasLie GroupsFinite-dimensional Lie AlgebrasLie Algebra Theory
In 1940, P. Hall introduced the concept of isoclinism on the class of all groups. In the present article we study the notion of isoclinism on a pair of Lie algebras, which forms an equivalence relation and show that each equivalence class contains a stem pair of Lie algebras, which has minimal dimension among the finite dimensional pairs of Lie algebras. Finally, some more results are obtained when two isoclinic pairs of Lie algebras are given.
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