Nilradical of a Lie algebra
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In
ideal
, which is as large as possible.
The nilradical of a finite-dimensional Lie algebra is its maximal nilpotent ideal, which exists because the sum of any two nilpotent ideals is nilpotent. It is an ideal in the radical of the Lie algebra . The quotient of a Lie algebra by its nilradical is a reductive Lie algebra . However, the corresponding
short exact sequence
does not split in general (i.e., there isn't always a subalgebra complementary to in ). This is in contrast to the Levi decomposition: the short exact sequence
does split (essentially because the quotient is semisimple).
See also
- Levi decomposition
- Nilradical of a ring, a notion in ring theory.
References
- OCLC 246650103.
- ISBN 978-3-540-54683-2.