theorem A.376 $\mathfrak{su}(3)$ is simple
open in the book ·
appendices/A-long-proofs.tex:18424
· p. 2975
Rests on
-
depends_on
definition A.375
Simple Lie algebra
¶
- depends_on definition 14.49 The special unitary group in three dimensions ¶
- depends_on definition 14.49 The special unitary group in three dimensions ¶ ↺
-
depends_on
proposition 14.50
Dimension and rank
¶
- depends_on definition 14.20 Cartan subalgebra and rank ¶
- depends_on definition 14.49 The special unitary group in three dimensions ¶ ↺
- proves proof ch:12-lie-groups-fibre-bundles@proof-21 ¶
- proves proof app:A-long-proofs@proof-231 ¶
Supports
- depends_on corollary A.377 The adjoint representation is irreducible ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Simple Lie algebra | declared | appendices/A-long-proofs.tex:18429 |
depends_on |
→ | The special unitary group in three dimensions | declared | appendices/A-long-proofs.tex:18429 |
depends_on |
→ | Dimension and rank | declared | appendices/A-long-proofs.tex:18429 |
depends_on |
← | The adjoint representation is irreducible | declared | appendices/A-long-proofs.tex:18438 |
proves |
← | app:A-long-proofs@proof-231 | declared | appendices/A-long-proofs.tex:18642 |