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In mathematics, the nilpotent cone N {\displaystyle {\mathcal {N}}} of a finite-dimensional semisimple Lie algebra g {\displaystyle {\mathfrak {g}}} is the set of elements that act nilpotently in all representations of g . {\displaystyle {\mathfrak {g}}.} In other words,
The nilpotent cone is an irreducible subvariety of g {\displaystyle {\mathfrak {g}}} .
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