proposition 14.36 Closed form of the exponential
open in the book ·
parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1407
· p. 557
Rests on
- depends_on equation 14.28 eq:lie-expso2 ¶
-
depends_on
proposition 14.35
Generators of $\mathfrak{su}(2)$
¶
- depends_on definition 14.32 The special unitary group in two dimensions ¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-13 ¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-14 ¶
Supports
- depends_on proposition 14.45 Which representations descend to $\SO(3,\R)$ ¶
-
depends_on
theorem 14.37
$\SU(2)$ is a two-to-one cover of $\SO(3,\R)$
¶
-
depends_on
corollary 14.38
$\SU(2)$ is the universal cover
¶
-
depends_on
proposition 14.31
$\SO(3,\R)$ is not simply connected
¶
- depends_on remark 29.12 The coordinate singularity, and what it is not ¶
- depends_on proposition 14.45 Which representations descend to $\SO(3,\R)$ ¶ ↺
-
depends_on
proposition 14.31
$\SO(3,\R)$ is not simply connected
¶
- depends_on lemma A.369 $\Phi$ is a two-sheeted covering ¶
-
depends_on
corollary 14.38
$\SU(2)$ is the universal cover
¶
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 |
→ | eq:lie-expso2 | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1418 |
depends_on |
→ | Generators of $\mathfrak{su}(2)$ | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1418 |
depends_on |
← | Which representations descend to $\SO(3,\R)$ | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1802 |
depends_on |
← | $\SU(2)$ is a two-to-one cover of $\SO(3,\R)$ | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1451 |
proves |
← | ch:12-lie-groups-fibre-bundles@proof-14 | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1421 |