definition A.325 Symmetric algebra and symbol
open in the book ·
appendices/A-long-proofs.tex:15967
· p. 2950
- ground object -- no derivation owed
Rests on
-
depends_on
definition A.320
Filtration by degree
¶
-
depends_on
definition 14.5
Universal enveloping algebra
¶
-
depends_on
equation 14.5
eq:lie-structconst
¶
-
step_from
equation 14.4
eq:lie-gengrlie
¶
- step_from equation 14.3 eq:lie-generators ¶
- step_from equation 14.2 eq:lie-varincor ¶
-
step_from
equation 14.4
eq:lie-gengrlie
¶
-
depends_on
equation 14.5
eq:lie-structconst
¶
-
depends_on
definition 14.5
Universal enveloping algebra
¶
-
depends_on
theorem A.319
Poincaré–Birkhoff–Witt
¶
- depends_on definition 14.5 Universal enveloping algebra ¶ ↺
- depends_on equation 14.12 eq:lie-uea-relations ¶
- proves proof app:A-long-proofs@proof-198 ¶
Supports
- depends_on corollary A.328 The Casimir elements are not accidentally zero ¶
-
depends_on
definition A.326
Symmetrization
¶
-
depends_on
proposition A.327
Symmetrization is an isomorphism of
$\mathfrak{g}$-modules
¶
-
depends_on
proposition A.348
Symmetrization identifies the invariants
¶
- depends_on lemma A.349 Lifting generators through the filtration ¶
-
depends_on
proposition A.348
Symmetrization identifies the invariants
¶
-
depends_on
proposition A.327
Symmetrization is an isomorphism of
$\mathfrak{g}$-modules
¶
- depends_on lemma A.349 Lifting generators through the filtration ¶ ↺
- depends_on proposition A.327 Symmetrization is an isomorphism of $\mathfrak{g}$-modules ¶ ↺
- depends_on proposition A.348 Symmetrization identifies the invariants ¶ ↺
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 |
→ | Filtration by degree | declared | appendices/A-long-proofs.tex:15990 |
depends_on |
→ | Poincaré–Birkhoff–Witt | declared | appendices/A-long-proofs.tex:15990 |
depends_on |
← | The Casimir elements are not accidentally zero | declared | appendices/A-long-proofs.tex:16081 |
depends_on |
← | Symmetrization | declared | appendices/A-long-proofs.tex:16005 |
depends_on |
← | Lifting generators through the filtration | declared | appendices/A-long-proofs.tex:17012 |
depends_on |
← | Symmetrization is an isomorphism of $\mathfrak{g}$-modules | declared | appendices/A-long-proofs.tex:16021 |
depends_on |
← | Symmetrization identifies the invariants | declared | appendices/A-long-proofs.tex:16971 |