I'm doing a project in algebraic geometry where Borel subgroups play a very important role, but my supervisor made a comment that confused me.
Let $G$ be a semisimple algebraic group and let $T\subset G$ be a maximal torus. Consider a borel subgroup $B$ containing $T$ and let $\phi$ be the set of roots of $G$ with respect to $T$. My supervisor said that $B$ can be partitioned into $\phi^+$ and $\phi^-$ but I haven't been able to find this in any book or article so my question is: How accurate is this statement? And if it isn't accurate, what would be a more correct interpretation?
Any help would be greatly appreciated.