Nonassociative rings and algebras Semisimple Lie algebras Concept
Compact real form
Summary
A compact real form of a complex semisimple Lie algebra is a real form whose Killing form is negative definite. These are exactly the real forms that are Lie algebras of compact Lie groups. Every complex semisimple Lie algebra has a compact real form, unique up to conjugation by an automorphism. This underlies Weyl's unitary trick and the Cartan decomposition.
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About this page
| Tag | 6QQF55DQ6K |
|---|---|
| URI | m2://6QQF55DQ6K |
| Kind | concept |
| Writing | W0 stub |
| MSC | 17B20, 22E60, 22E46 |
| Specializes | Real form |
| Changed | 3 November 2026 |
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