About: Regular element of a Lie algebra

In mathematics, a regular element of a Lie algebra or Lie group is an element whose centralizer has dimension as small as possible.For example, in a complex semisimple Lie algebra, an element is regular if its centralizer in has dimension equal to the rank of , which in turn equals the dimension of some Cartan subalgebra (note that in earlier papers, an element of a complex semisimple Lie algebra was termed regular if it is semisimple and the kernel of its adjoint representation is a Cartan subalgebra).An element a Lie group is regular if its centralizer has dimension equal to the rank of .