Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:characterizedBy |
determinant nonzero
diagonal entries equal to 2 integer entries off-diagonal entries less than or equal to 0 |
| gptkbp:dimensions |
n \\times n matrix
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cartan matrices
|
| gptkbp:namedAfter |
gptkb:Élie_Cartan
|
| gptkbp:relatedTo |
gptkb:Dynkin_diagrams
gptkb:generalized_Cartan_matrices |
| gptkbp:satisfies |
a_{ii} = 2
a_{ij} = 0 \\implies a_{ji} = 0 a_{ij} \\in \\mathbb{Z} a_{ij} \\leq 0 for i \\neq j |
| gptkbp:used_in |
gptkb:Kac–Moody_algebras
representation theory root systems Lie algebra theory classification of simple Lie algebras theory of algebraic groups |
| gptkbp:used_to_classify |
gptkb:semisimple_Lie_algebras
|
| gptkbp:bfsParent |
gptkb:Dynkin_diagrams
|
| gptkbp:bfsLayer |
7
|