Theorems · Theorem · nonassociative algebras

RootPairing.GeckConstruction.trace_h_eq_zero

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [CharZero R] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [inst_4 : AddCommGroup N] [inst_5 : Module R N] {P : RootPairing ι R M N}
  [inst_6 : P.IsCrystallographic] {b : P.Base} [inst_7 : Fintype ι] (i : ↥b.support),
  (RootPairing.GeckConstruction.h i).trace = 0

Defined in: Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple
Cited by: 1 results in Mathlib
Foundations: Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CharZero AddCommGroup Module AddCommGroup Module RootPairing.IsCrystallographic Fintype

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Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
Finsetstatement · cited by 13,712
AddCommGroupstatement and proof · cited by 12,871
Equivproof · cited by 8,337
Fintypestatement and proof · cited by 7,736
Finset.sumproof · cited by 5,195
Finset.univproof · cited by 3,473
zero_addproof · cited by 2,366
Finset.sum_congrproof · cited by 2,323
Nat.cast_zeroproof · cited by 1,870
CharZerostatement and proof · cited by 932

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RootPairing.GeckConstruction.trace_toEnd_eq_zeroproof · cited by 0