On Commutative Polarizations

Details On Commutative Polarizations On Commutative Polarizations

2003-02-19

arxiv.org/abs/math/0302229v1

Mathematics

Representation Theory

34 pages, 2 figures. Submitted to Journal of Algebra

Scientific paper

The purpose of this paper is to study finite-dimensional Lie algebras over a
field k of characteristic zero which admit a commutative polarization (CP).
Among the many results and examples, it is shown that, if k is algebraically
closed, the nilradical N of a parabolic subalgebra in A_n and C_n has such a
CP. Using this fact a simple closed formula is derived for the index of N.

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