The index of a Lie algebra, the centralizer of a nilpotent element, and the normalizer of the centralizer

By Dmitri I. Panyushev. Mathematical Proceedings of the Cambridge Philosophical Society, 2001

70 citations recorded by the source corpus.

Let ${\rm q}$ be a Lie algebra and ξ a linear form on ${\rm q}$. Denote by ${\rm q}_{\xi}$ the set of all $x \in {\rm q}$ such that $\xi([{\rm q},x]) = 0$. In other words, ${\rm q}_{\xi}=\{x\in {\rm q} \mid({\rm ad}^*x)\cdot = 0\}$, where ${\rm ad}^*: {\rm q}\rightarrow {\rm g I}({\rm q}^*)$ is the coadjoint representation of ${\rm q}$. The index of ${\rm q}$, ind ${\rm q}$, is defined by \[ {\rm ind\, q} = \min_{\xi\in {\rm q}^*}\dim {\rm q}\xi. \]

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82bc17ffe5fa471fe3cced1d5ebba1f453702e74

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On symmetric invariants of centralisers in reductive Lie algebras (2006, background): “For the spherical nilpotent orbits, Elashvili’s conjecture was proved in [17] and [18] by the first author.”