The nilpotent cone of a complex semisimple Lie algebra 
is the algebraic
set of 
for which 
is nilpotent. It includes zero and is a union of adjoint orbits. For 
, writing 
gives
 |
This affine quadratic cone is singular at zero (Fu 2006).
Nilpotent Cone
See also
Global Nilpotent Cone, Lie Algebra, Nilpotent Matrix, Symplectic SingularityExplore with Wolfram|Alpha
References
Fu, B. "A Survey on Symplectic Singularities and Symplectic Resolutions." Ann. Math. Blaise Pascal 13, 209-236, 2006. https://doi.org/10.5802/ambp.218.Cite this as:
Weisstein, Eric W. "Nilpotent Cone." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NilpotentCone.html