Theorems · Inductive type · nonassociative algebras

LieSubalgebra

(R : Type u) → (L : Type v) → [inst : CommRing R] → [inst_1 : LieRing L] → [LieAlgebra R L] → Type v

A Lie subalgebra of a Lie algebra is submodule that is closed under the Lie bracket. This is a sufficient condition for the subset itself to form a Lie algebra.

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

418 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 4 definitions · uses no axioms

Assumes

CommRingLieRingLieAlgebra