English

On derivations of parabolic Lie algebras

Rings and Algebras 2015-11-03 v3

Abstract

Let g\mathfrak{g} be a reductive Lie algebra over an algebraically closed, characteristic zero field or over R\mathbb{R}. Let q\mathfrak{q} be a parabolic subalgebra of g\mathfrak{g}. We characterize the derivations of q\mathfrak{q} by decomposing the derivation algebra as the direct sum of two ideals: one of which being the image of the adjoint representation and the other consisting of all linear transformations on q\mathfrak{q} that map into the center of q\mathfrak{q} and map the derived algebra of q\mathfrak{q} to 00.

Keywords

Cite

@article{arxiv.1504.08286,
  title  = {On derivations of parabolic Lie algebras},
  author = {Daniel Brice},
  journal= {arXiv preprint arXiv:1504.08286},
  year   = {2015}
}