Lie Groups¶
- class sage.categories.lie_groups.LieGroups(base, name=None)[source]¶
- Bases: - Category_over_base_ring- The category of Lie groups. - A Lie group is a topological group with a smooth manifold structure. - EXAMPLES: - sage: from sage.categories.lie_groups import LieGroups sage: C = LieGroups(QQ); C Category of Lie groups over Rational Field - >>> from sage.all import * >>> from sage.categories.lie_groups import LieGroups >>> C = LieGroups(QQ); C Category of Lie groups over Rational Field - additional_structure()[source]¶
- Return - None.- Indeed, the category of Lie groups defines no new structure: a morphism of topological spaces and of smooth manifolds is a morphism as Lie groups. - See also - EXAMPLES: - sage: from sage.categories.lie_groups import LieGroups sage: LieGroups(QQ).additional_structure() - >>> from sage.all import * >>> from sage.categories.lie_groups import LieGroups >>> LieGroups(QQ).additional_structure() 
 - super_categories()[source]¶
- EXAMPLES: - sage: from sage.categories.lie_groups import LieGroups sage: LieGroups(QQ).super_categories() [Category of topological groups, Category of smooth manifolds over Rational Field] - >>> from sage.all import * >>> from sage.categories.lie_groups import LieGroups >>> LieGroups(QQ).super_categories() [Category of topological groups, Category of smooth manifolds over Rational Field]