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

sage: from sage.categories.lie_groups import LieGroups
sage: C = LieGroups(QQ); C
Category of Lie groups over Rational Field

Python

>>> 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

Category.additional_structure()

EXAMPLES:

Sage

sage: from sage.categories.lie_groups import LieGroups
sage: LieGroups(QQ).additional_structure()

Python

>>> from sage.all import *
>>> from sage.categories.lie_groups import LieGroups
>>> LieGroups(QQ).additional_structure()

super_categories()[source]#

EXAMPLES:

Sage

sage: from sage.categories.lie_groups import LieGroups
sage: LieGroups(QQ).super_categories()
[Category of topological groups,
 Category of smooth manifolds over Rational Field]

Python

>>> 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]