Abelian Lie Algebras

AUTHORS:

  • Travis Scrimshaw (2016-06-07): Initial version
sage.algebras.lie_algebras.abelian.AbelianLieAlgebra

An abelian Lie algebra.

A Lie algebra \(\mathfrak{g}\) is abelian if \([x, y] = 0\) for all \(x, y \in \mathfrak{g}\).

EXAMPLES:

sage: L.<x, y> = LieAlgebra(QQ, abelian=True)
sage: L.bracket(x, y)
0
sage.algebras.lie_algebras.abelian.InfiniteDimensionalAbelianLieAlgebra

An infinite dimensional abelian Lie algebra.

A Lie algebra \(\mathfrak{g}\) is abelian if \([x, y] = 0\) for all \(x, y \in \mathfrak{g}\).