English
For a finite free Lie module M, the coefficients of the characteristic polynomial of the bracket operator are polynomial in x; the rank is the first nonzero coefficient.
Русский
Для конечной свободной Ли-модули коэффициенты характеристического многочлена оператора скобки зависят от x; ранг равен первой ненулевой коэффициенте.
LaTeX
$$polyCharpoly_coeff_rank_ne_zero$$
Lean4
/-- Let `M` be a representation of a Lie algebra `L` over a nontrivial commutative ring `R`,
and assume that `L` and `M` are finite free as `R`-module.
Then the coefficients of the characteristic polynomial of `⁅x, ·⁆` are polynomial in `x`.
The *rank* of `M` is the smallest `n` for which the `n`-th coefficient is not the zero polynomial.
-/
noncomputable def rank : ℕ :=
nilRank φ
