In mathematics, the nilpotent cone of a finite-dimensional semisimple Lie algebra is the set of elements that act nilpotently in all representations of In other words, The nilpotent cone is an irreducible subvariety of (considered as a vector space). Example The nilpotent cone of , 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 References . . Lie algebras