Lie algebra

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Lie algebra

[′lē ‚al·jə·brə]
(mathematics)
The algebra of vector fields on a manifold with additive operation given by pointwise sum and multiplication by the Lie bracket.
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Given a nilpotent Lie algebra L of dimension dim L = n, it is well-known that the second homology Lie algebra [H.
However the following three bounds are true for a nilpotent Lie algebra L of dim L = n (see [8, 10, 15, 16, 24]):
In order to state one of his results, we recall that the type of a finite dimensional nilpotent Lie algebra L of class c is defined as the c-tuple ([m.
Let L be a nilpotent Lie algebra of dim L = n, dim [L.
Let L be a finite dimensional nilpotent Lie algebra and N an ideal of L of dim N = k and dim L/ N = u.
Then a nilpotent Lie algebra has a natural filtration given by the central descending sequence: G = [C.
An n-dimensional nilpotent Lie algebra is called filiform if its nilindex p = n [right arrow] 1.
Thus an n-dimensional nilpotent Lie algebra is filiform if its characteristic sequence is of the form c (G) = (n - 1, 1).
Section 4 is dedicated to nilpotent Lie algebras and specially to filiform Lie algebras.
Q] be a nilpotent Lie algebra with rational structure constants; i.
Q]\k is a nilpotent Lie algebra, and its image under exp is a group which is isomorphic to [G.
The contributors investigate alternating triple systems with simple Lie algebras of derivations, simple decompositions of simple Lie superalgebras, generalized capable abelian groups, Freudenthal's magic square, and Vinberg algebras associated to some nilpotent Lie algebras.