Map · 17
nonassociative algebras
MSC 17 · Nonassociative rings and algebras
4,141 declarations (3,021 theorems, 1,120 definitions) across 97 files. 0 of the 9 famous theorems listed for this area are in Mathlib (0%). 2 open conjectures here are stated in Lean.
Files are assigned to areas by a language model reading each file's documentation. Report a file that is in the wrong area.
Subareas3
- 17B Lie algebras and Lie superalgebras 3,502
- 17A General nonassociative rings 619
- 17C Jordan algebras (algebras, triples and pairs) 20
Famous theorems0 of 9
From the 1000+ theorems project, which classifies each theorem by MSC area.
Open conjectures stated in Lean2
Statements without proofs, collected by the Formal Conjectures project.
Structures defined here24
Typeclasses defined in this area's files, most assumed first.
- LieRing 2,345
- LieAlgebra 1,947
- LieRingModule 1,128
- LieModule 577
- LieSubalgebra.IsCartanSubalgebra 149
- LieModule.IsTriangularizable 144
- LieAlgebra.IsKilling 142
- RootPairing.IsValuedIn 118
- RootPairing.IsRootSystem 64
- RootPairing.IsReduced 56
- RootPairing.EmbeddedG2 52
- RootPairing.IsIrreducible 40
- RootPairing.IsAnisotropic 33
- LieModule.IsNilpotent 27
- LieModule.LinearWeights 26
- LieRinehartRing 19
- LieAlgebra.IsSolvable 16
- Bracket 13
- LieRinehartAlgebra 13
- GradedLieAlgebra 12
- LieAlgebra.IsSimple 12
- LieDerivation.SMulBracketCommClass 11
- IsJordan 10
- RootPairing.IsBalanced 10
Files97
Largest first. The code after each file is its assigned subarea.
- Mathlib.Algebra.Lie.Basic
Lie algebras
17B · 285
- Mathlib.Algebra.Algebra.NonUnitalSubalgebra
Non-unital Subalgebras over Commutative Semirings
17A · 225
- Mathlib.Algebra.Lie.Submodule
Lie submodules of a Lie algebra
17B · 200
- Mathlib.Algebra.Lie.Subalgebra
Lie subalgebras
17B · 153
- Mathlib.LinearAlgebra.RootSystem.Defs
Root data and root systems
17B · 136
- Mathlib.LinearAlgebra.RootSystem.Hom
Morphisms of root pairings
17B · 125
- Mathlib.Algebra.Ring.CentroidHom
Centroid homomorphisms
17A · 114
- Mathlib.Algebra.Lie.Nilpotent
Nilpotent Lie algebras
17B · 109
- Mathlib.Algebra.Lie.Weights.Basic
Weight spaces of Lie modules of nilpotent Lie algebras
17B · 107
- Mathlib.Algebra.Algebra.NonUnitalHom
Morphisms of non-unital algebras
17A · 98
- Mathlib.LinearAlgebra.RootSystem.Finite.G2
Properties of the `𝔤₂` root system.
17B · 87
- Mathlib.Algebra.Lie.Extension
Extensions of Lie algebras
17B · 85