smoothRightMul — Mathlib

English

For fixed g ∈ G, the left multiplication operator L_g acts on h by L_g(h) = g h.

Русский

Для фиксированного g ∈ G left multiplication оператор действует на h так, что L_g(h) = g h.

LaTeX

$$$L\_I g (h) = g h$$$

Lean4

/-- Right multiplication by `g`. It is meant to mimic the usual notation in Lie groups.
Used mostly through the notation `𝑹`.
Lemmas involving `smoothRightMul` with the notation `𝑹` usually use `R` instead of `𝑹` in the
names. -/
def smoothRightMul : C^∞⟮I, G; I, G⟯ :=
  ⟨(· * g), contMDiff_mul_right⟩
    -- Left multiplication. The abbreviation is `MIL`.

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