proposition 15.62 The complex line is not a semigroup algebra

open in the book · parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2308 · p. 626

Rests on

depends_on definition 4.18 Semigroup ¶
- depends_on definition 4.6 Associativity ¶
  - depends_on definition 4.3 Algebraic structure ¶
    - depends_on definition 4.2 Binary operation ¶
      - depends_on definition 4.1 Cartesian product ¶
      - depends_on definition 3.43 Map ¶
- depends_on definition 4.4 Internal binary operation; magma ¶
  - depends_on definition 4.3 Algebraic structure ¶ ↺
  - depends_on definition 4.2 Binary operation ¶ ↺
depends_on proposition 15.60 Semigroup expansion ¶
- depends_on definition 15.3 Tensor product Lie algebra ¶
- depends_on theorem 15.4 The construction produces a Lie algebra ¶
  - depends_on definition 15.3 Tensor product Lie algebra ¶ ↺
  - proves proof ch:13-lie-algebra-expansions@proof-1 ¶
- proves proof ch:13-lie-algebra-expansions@proof-34 ¶
proves proof ch:13-lie-algebra-expansions@proof-35 ¶

Supports

depends_on remark 15.63 The inclusion is strict, and the strictness is physical ¶

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`	→	Semigroup	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2311
`depends_on`	→	Semigroup expansion	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2311
`depends_on`	←	The inclusion is strict, and the strictness is physical	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2358
`proves`	←	ch:13-lie-algebra-expansions@proof-35	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2314