A Cartan subgroup of a connected Lie group is a closed nilpotent group that is a subgroup
whose Lie algebra is a Cartan
subalgebra and which has finite subgroup index
in its normalizer. For a connected complex reductive
algebraic group, Cartan subgroups are maximal
tori in the algebraic-group sense, isomorphic to 
, and are conjugate. Here 
denotes the nonzero complex
numbers under multiplication.
Cartan Subgroup
See also
Lie Group, Maximal Torus, Nilpotent GroupExplore with Wolfram|Alpha
References
Knapp, A. W. Lie Groups Beyond an Introduction, 2nd ed. Boston, MA: Birkhäuser, 2002.Cite this as:
Weisstein, Eric W. "Cartan Subgroup." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CartanSubgroup.html