A maximal torus of a compact connected Lie group 
is a torus 
that is not properly contained
in any larger torus in 
.
Every element of 
belongs to a maximal torus, and any two maximal tori are conjugate. Their common
dimension is the rank of 
.
Maximal Torus
See also
Lie Group, Maximal Tori Theorem, TorusExplore with Wolfram|Alpha
References
Bröcker, T. and tom Dieck, T. Representations of Compact Lie Groups. New York: Springer-Verlag, 1985.Cite this as:
Weisstein, Eric W. "Maximal Torus." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MaximalTorus.html