Theorems · Definition · nonassociative algebras

LieAlgebra.IsKilling.corootSubmodule

{K : Type u_2} →
  {L : Type u_3} →
    [inst : LieRing L] →
      [inst_1 : Field K] →
        [inst_2 : LieAlgebra K L] →
          [FiniteDimensional K L] →
            {H : LieSubalgebra K L} →
              [inst_4 : H.IsCartanSubalgebra] → LieModule.Weight K (↥H) L → LieSubmodule K (↥H) L

The coroot space of α viewed as a submodule of the ambient Lie algebra L. This represents the image of the coroot space under the inclusion H ↪ L.

Defined in

Mathlib.Algebra.Lie.Weights.Killing

Cited by

7 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingFieldLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebra