Kac-Moody Algebras¶
AUTHORS:
Travis Scrimshaw (07-15-2017): Initial implementation
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class
sage.categories.kac_moody_algebras.
KacMoodyAlgebras
(base, name=None)¶ Bases:
sage.categories.category_types.Category_over_base_ring
Category of Kac-Moody algebras.
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class
ParentMethods
¶ Bases:
object
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cartan_type
()¶ Return the Cartan type of
self
.EXAMPLES:
sage: L = LieAlgebra(QQ, cartan_type=['A', 2]) sage: L.cartan_type() ['A', 2]
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weyl_group
()¶ Return the Weyl group of
self
.EXAMPLES:
sage: L = LieAlgebra(QQ, cartan_type=['A', 2]) sage: L.weyl_group() Weyl Group of type ['A', 2] (as a matrix group acting on the ambient space)
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example
(n=2)¶ Return an example of a Kac-Moody algebra as per
Category.example
.EXAMPLES:
sage: from sage.categories.kac_moody_algebras import KacMoodyAlgebras sage: KacMoodyAlgebras(QQ).example() Lie algebra of ['A', 2] in the Chevalley basis
We can specify the rank of the example:
sage: KacMoodyAlgebras(QQ).example(4) Lie algebra of ['A', 4] in the Chevalley basis
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super_categories
()¶ EXAMPLES:
sage: from sage.categories.kac_moody_algebras import KacMoodyAlgebras sage: KacMoodyAlgebras(QQ).super_categories() [Category of Lie algebras over Rational Field]
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class