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compact Lie algebra
Contents
Context
-Lie theory
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Cohomology
Homotopy
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
Contents
Definition
A semisimple Lie algebra is compact if its Killing form is a negative definite bilinear form.
Properties
A proof is spelled out for instance in (Woit, theorem 1).
References
For instance
- Peter Woit, Topics in Representation Theory: The Killing Form, Reflections and Classification of Root Systems (pdf)
Last revised on September 14, 2011 at 18:35:53.
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