 Borel subalgebra

For a choice of positive roots, the corresponding Borel subalgebra is $\mathfrak{b}=\mathfrak{t}\oplus {\mathfrak{n}}^{+}$, the sum of a Cartan subalgebra and all positive root spaces.

In the context of Lie theory, a **Borel subalgebra** is a type of subalgebra of a Lie algebra that has certain important properties. Specifically, for a complex semisimple Lie algebra \(\mathfrak{g}\), a Borel subalgebra is a maximal solvable subalgebra.