Search results for " 17B99"

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A note on the Schur multiplier of a nilpotent Lie algebra

2011

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong H(1)\oplus A$, where $A$ is an abelian Lie algebra of dimension $n-3$ and H(1) is the Heisenberg algebra of dimension 3.

Pure mathematicsAlgebra and Number TheoryDimension (graph theory)Schur multiplier nilpotent Lie algebrasMathematics - Rings and AlgebrasUpper and lower boundsNilpotent Lie algebraSettore MAT/02 - Algebra17B30 17B60 17B99Rings and Algebras (math.RA)Lie algebraFOS: MathematicsSettore MAT/03 - GeometriaAlgebra over a fieldAbelian groupMathematicsSchur multiplier
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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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