Lie algebra

(redirected from Abelian Lie algebra)

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.
References in periodicals archive ?
The Schur multiplier of the pair (L, N), where L is a Lie algebra with ideal, is the abelian Lie algebra M(L, N) which appears in the following natural exact sequence of Mayer-Vietoris type
We recall that A(n) denotes the abelian Lie algebra of dimension n and the main results of [2, 5, 6, 7, 11, 18, 19] illustrate that many inequalities on dim M(L) become equalities if and only if L splits in the sums of A(n) and of a Heisenberg algebra H(m) (here m [greater than or equal to] 1 is a given integer).
Since N/N [intersection] [PHI](L) [congruent] A(t) is a direct factor of the abelian Lie algebra L/[PHI](L) [congruent] A(s + t) [congruent] A(s) [direct sum] A(t), Lemma 2.
The dimension of the Schur multiplier of abelian Lie algebras is a classic.
By the classical Lie theory, the Lie algebra of a compact Lie group is a direct product of an abelian Lie algebra and some simple Lie algebras.
The index of an n-dimensional Abelian Lie algebra is n.
An Abelian Lie algebra L spanned by the vector fields [Z.