regular element of a Lie algebra
Regular elements clearly exist and moreover they are Zariski dense in . The function is an upper semi-continuous function . Indeed, it is a constant minus and is lower semi-continuous. Thus the set of elements whose centralizer dimension is (greater than or) equal to that of any given regular element is Zariski open and non-empty.
If is reductive then the minimal centralizer dimension is equal to the rank of .
|Title||regular element of a Lie algebra|
|Date of creation||2013-03-22 15:30:53|
|Last modified on||2013-03-22 15:30:53|
|Last modified by||benjaminfjones (879)|