cartanEquivDual — Mathlib

English

CartanEquivDual provides a linear equivalence between a Cartan subalgebra and its dual space, interpolating trace forms.

Русский

CartanEquivDual задаёт линейное отображение между Cartan-subalgebra и его двойственным пространством, связанное с формами следа.

LaTeX

$$$ cartanEquivDual\\;H : H \\to^{\\text{linear}} H^* $$$

Lean4

/-- The restriction of the Killing form to a Cartan subalgebra, as a linear equivalence to the
dual. -/
@[simps! apply_apply]
noncomputable def cartanEquivDual : H ≃ₗ[K] Module.Dual K H :=
  (traceForm K H L).toDual <| traceForm_cartan_nondegenerate K L H

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