proposition 15.60 Semigroup expansion

open in the book · parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2268 · p. 625

Rests on

Supports

Neighborhood

Every logical edge within two steps of this node.

proposition 15.60: Semigroup expansion15.60definition 15.3: Tensor product Lie algebra15.3theorem 15.4: The construction produces a Lie algebra15.4proposition 15.62: The complex line is not a semigroup algebra15.62proof : ch:13-lie-algebra-expansions@proof-34proofdefinition 15.52: Balanced form15.52definition 15.14: Truncated polynomial algebra and Takiff algebra15.14example 15.61: Maurer–Cartan expansion15.61proposition 15.6: Functoriality15.6proposition 15.41: Resonance, general form15.41proposition 15.7: Ideals of A become ideals of g_A15.7proposition 15.8: The radical of A is solvable in g_A15.8proposition 15.15: Takiff brackets15.15theorem 15.13: Classification of g_A by the algebra15.13theorem 15.54: Completeness in the bilinear case15.54theorem 15.29: The three constant-curvature kinematics, in every dimension15.29theorem 15.51: Factorisation of invariant forms15.51theorem 15.10: Factorisation of the Killing form15.10proof : ch:13-lie-algebra-expansions@proof-1proofdefinition 4.18: Semigroup4.18remark 15.63: The inclusion is strict, and the strictness is physical15.63proof : ch:13-lie-algebra-expansions@proof-35proof

Edges

typedirectionnode provenancewhere
cites Expanding Lie (super)algebras through Abelian semigroups derived parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2273
depends_on Tensor product Lie algebra declared parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2281
depends_on The construction produces a Lie algebra declared parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2281
depends_on The complex line is not a semigroup algebra declared parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2311
proves ch:13-lie-algebra-expansions@proof-34 declared parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2284