DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

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The regular root-hyperplane arrangement in a Cartan subalgebra

Definition

Let $h$ be a Cartan subalgebra of a complex semisimple Lie algebra with root set $Φ$ from Root-space decomposition relative to a Cartan subalgebra. The regular root-hyperplane arrangement in $h$ is the complement

$h_{r e g} : = {h \in h : α (h) \neq 0 for every α \in Φ} .$

Equivalently, $h_{r e g}$ is obtained from $h$ by removing the finitely many root hyperplanes $\ker α$ .

Depends on

Root-space decomposition relative to a Cartan subalgebra

Used by

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Pavel Etingof, Lie Groups and Lie Algebras I (standard reference, not scraped)