Structures · Algebra
LieAlgebra.IsSimple
A Lie algebra is simple if it is irreducible as a Lie module over itself via the adjoint action, and it is non-Abelian.
- Defined in
- Mathlib.Algebra.Lie.Semisimple.Defs
- Shape
- 2 explicit arguments · adds eq_bot_or_eq_top, non_abelian
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by0
Nothing extends this class yet.
Concrete types that are instances0
No instance on a concrete type; it is reached through other classes.
How is a type an instance?
Loading the hierarchy index…
Assumed by11
- LieAlgebra.IsSimple.non_abelian
- LieAlgebra.IsSimple.eq_bot_or_eq_top
- LieAlgebra.Basis.equivOfReindex
- LieAlgebra.IsSimple.instIsSemisimple
- LieAlgebra.IsSimple.eq_top_of_isAtom
- LieAlgebra.IsSimple.isAtom_iff_eq_top
- LieAlgebra.instIsIrreducibleRootSystem_of_isSimple
- LieAlgebra.IsSimple.instHasTrivialRadical
- LieAlgebra.IsSimple.instIsIrreducible
- LieAlgebra.IsSimple.isAtom_top
- LieAlgebra.IsSimple.nontrivial
Ancestors0
No ancestors.