Theorems · Theorem · nonassociative algebras
LieSubalgebra.coe_bracket_of_module
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (L' : LieSubalgebra R L)
{M : Type w} [inst_3 : AddCommGroup M] [inst_4 : LieRingModule L M] (x : ↥L') (m : M), ⁅x, m⁆ = ⁅↑x, m⁆- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketstatement · cited by 642
- LieSubalgebrastatement and proof · cited by 418
Cited by8
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.finrank_rootSpace_eq_oneproof · cited by 6
- IsSl2Triple.h_eq_corootproof · cited by 4
- LieIdeal.coe_bracket_of_moduleproof · cited by 4
- LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_corootproof · cited by 2
- LieIdeal.coe_lcs_eqproof · cited by 1
- LieAlgebra.zeroRootSubalgebra_normalizer_eq_selfproof · cited by 1
- LieSubalgebra.normalizer_eq_self_iffproof · cited by 1
- LieModule.trace_toEnd_genWeightSpaceChain_eq_zeroproof · cited by 1