Nilpotent cone

In mathematics, the nilpotent cone formula_1 of a finite-dimensional semisimple Lie algebra formula_2 is the set of elements that act nilpotently in all representations of formula_3 In other words, 
The nilpotent cone is an irreducible subvariety of formula_2 (considered as a vector space).
Example.
The nilpotent cone of formula_6, the Lie algebra of 2×2 matrices with vanishing trace, is the variety of all 2×2 traceless matrices with rank less than or equal to formula_7