nilpotent cone
Let be a finite dimensional semisimple Lie algebra. The
nilpotent cone of is the set of elements that
act nilpotently in all representations of . In other words,
The nilpotent cone is an irreducible (http://planetmath.org/IrreducibleClosedSet)
subvariety (http://planetmath.org/AffineVariety) of (considered as a
-vector space), and is invariant under the adjoint action of
on itself.
Example: if , then the nilpotent cone
is the variety of all matrices in with rank .
Title | nilpotent cone |
---|---|
Canonical name | NilpotentCone |
Date of creation | 2013-03-22 13:58:36 |
Last modified on | 2013-03-22 13:58:36 |
Owner | rmilson (146) |
Last modified by | rmilson (146) |
Numerical id | 9 |
Author | rmilson (146) |
Entry type | Definition |
Classification | msc 17B20 |
Synonym | nilcone |