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Cartan subalgebra

Contents

Context

\infty-Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Contents

Definition

For GG a compact Lie group with Lie algebra 𝔤\mathfrak{g}, a Cartan subalgebra of 𝔤\mathfrak{g} is a sub-Lie algebra

𝔱𝔤 \mathfrak{t} \hookrightarrow \mathfrak{g}

that is the Lie algebra of a maximal torus

TG. T \hookrightarrow G \,.

More generally…

References

Last revised on January 10, 2017 at 11:15:19. See the history of this page for a list of all contributions to it.