The Bianchi variety
classification
🧮 math.DG
keywords
algebrastructuresvarietyactsalgebraicbianchicompatibilitydescription
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The totality Lie(V) of all Lie algebra structures on a vector space V over a field F is an algebraic variety over F on which the group GL(V) acts naturally. We give an explicit description of Lie(V) for dim V=3 which is based on the notion of compatibility of Lie algebra structures.
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