Borel subalgebra

In mathematics, specifically in representation theory, a Borel subalgebra of a Lie algebra ${\displaystyle {\mathfrak {g}}}$ is a maximal solvable subalgebra.^[1] The notion is named after Armand Borel.

If the Lie algebra ${\displaystyle {\mathfrak {g}}}$ is the Lie algebra of a complex Lie group, then a Borel subalgebra is the Lie algebra of a Borel subgroup.