Theorems · Theorem · nonassociative algebras
LieAlgebra.IsKilling.ker_killingForm_eq_bot
∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [LieAlgebra.IsKilling R L], LinearMap.ker (killingForm R L) = ⊥
- Defined in
- Mathlib.Algebra.Lie.Killing
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Submodulestatement · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LinearMap.kerstatement · cited by 848
- LieAlgebra.IsKillingstatement and proof · cited by 122
- LieSubalgebra.toSubmoduleproof · cited by 90
- LieIdeal.toLieSubalgebraproof · cited by 48
- killingFormstatement · cited by 34
Cited by7
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZeroproof · cited by 5
- LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpaceproof · cited by 3
- LieAlgebra.IsKilling.killingForm_nondegenerateproof · cited by 2
- LieDerivation.IsKilling.range_ad_eq_topproof · cited by 1
- LieAlgebra.isKilling_of_equivproof · cited by 1
- LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebraproof · cited by 1