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

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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

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  • Aoki, T.; Majima, H.; Takei, Y.; Tose, N. (2009), Algebraic Analysis of Differential Equations: from Microlocal Analysis to Exponential Asymptotics, Springer, p. 173, ISBN 9784431732402.
  • Anker, Jean-Philippe; Orsted, Bent (2006), Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, Progress in Mathematics, vol. 229, Birkhäuser, p. 166, ISBN 9780817644307.

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