Theorems · Definition · nonassociative algebras

RootPairing.restrictScalarsRat

{ι : Type u_1} →
  {L : Type u_2} →
    {M : Type u_3} →
      {N : Type u_4} →
        [inst : Field L] →
          [inst_1 : AddCommGroup M] →
            [inst_2 : AddCommGroup N] →
              [inst_3 : Module L M] →
                [inst_4 : Module L N] →
                  (P : RootPairing ι L M N) →
                    [P.IsBalanced] →
                      [inst_6 : CharZero L] →
                        [P.IsCrystallographic] →
                          RootPairing ι ℚ ↥(Submodule.span ℚ (Set.range ⇑P.root))
                            ↥(Submodule.span ℚ (Set.range ⇑P.coroot))

Restriction of scalars to ℚ for a crystallographic root pairing in characteristic zero.

Defined in

Mathlib.LinearAlgebra.RootSystem.BaseChange

Cited by

0 results in Mathlib

Foundations

Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupAddCommGroupModuleModuleRootPairing.IsBalancedCharZeroRootPairing.IsCrystallographic