0000000000925934

AUTHOR

Giovanni Moreno

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The Bianchi variety

2010

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.

Mathematics - Differential GeometryPure mathematicsSimple Lie groupAdjoint representationAffine Lie algebra13D10 14D99 17B99 53D99Graded Lie algebraLie conformal algebraAlgebraAdjoint representation of a Lie algebraLie coalgebraRepresentation of a Lie groupDifferential Geometry (math.DG)Computational Theory and MathematicsFOS: MathematicsGeometry and TopologyAnalysisMathematicsDifferential Geometry and its Applications
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