ToLieAlgebra — Mathlib

English

The Lie algebra associated to a Cartan matrix is defined as the free Lie algebra modulo the Cartan relations.

Русский

Ли-алгебра, ассоциированная с Картановой матрицей, определена как свободная Ли-алгебра по модулю реляций Картанa.

LaTeX

$$$\\text{ToLieAlgebra} := \\operatorname{FreeLieAlgebra}(R,[Generators]) / \\text{CartanMatrix.Relations.toIdeal } R A$$$

Lean4

/-- The Lie algebra corresponding to a Cartan matrix.

Note that it is defined for any matrix of integers. Its value for non-Cartan matrices should be
regarded as junk. -/
def ToLieAlgebra :=
  FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A
deriving LieRing, Inhabited, LieAlgebra R

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