def __init__(self, group, base_ring=IntegerRing()):
r"""
See :class:`GroupAlgebra` for full documentation.
EXAMPLES::
sage: GroupAlgebra(GL(3, GF(7)))
Group algebra of group "General Linear Group of degree 3 over Finite Field of size 7" over base ring Integer Ring
"""
from sage.groups.group import Group
from sage.groups.old import Group as OldGroup
if not base_ring.is_commutative():
raise NotImplementedError("Base ring must be commutative")
if not isinstance(group, (Group, OldGroup)):
raise TypeError('"%s" is not a group' % group)
self._group = group
CombinatorialFreeModule.__init__(self, base_ring, group,
prefix='',
bracket=False,
category=HopfAlgebrasWithBasis(base_ring))
if not base_ring.has_coerce_map_from(group) :
## some matrix groups assume that coercion is only valid to
## other matrix groups. This is a workaround
## call _element_constructor_ to coerce group elements
#try :
self._populate_coercion_lists_(coerce_list=[base_ring, group])
#except TypeError :
# self._populate_coercion_lists_( coerce_list = [base_ring] )
else :
self._populate_coercion_lists_(coerce_list=[base_ring])
def super_categories(self):
"""
EXAMPLES::
sage: FiniteDimensionalHopfAlgebrasWithBasis(QQ).super_categories()
[Category of finite dimensional bialgebras with basis over Rational Field, Category of hopf algebras with basis over Rational Field]
"""
R = self.base_ring()
return [FiniteDimensionalBialgebrasWithBasis(R), HopfAlgebrasWithBasis(R)]
def __init__(self, R, G):
"""
EXAMPLES::
sage: from sage.categories.examples.hopf_algebras_with_basis import MyGroupAlgebra
sage: A = MyGroupAlgebra(QQ, DihedralGroup(6))
sage: A.category()
Category of hopf algebras with basis over Rational Field
sage: TestSuite(A).run()
"""
self._group = G
CombinatorialFreeModule.__init__(self, R, G, category = HopfAlgebrasWithBasis(R))
def super_categories(self):
"""
EXAMPLES::
sage: GradedHopfAlgebrasWithBasis(QQ).super_categories()
[Category of graded bialgebras with basis over Rational Field, Category of graded hopf algebras over Rational Field, Category of hopf algebras with basis over Rational Field]
"""
R = self.base_ring()
return [
GradedBialgebrasWithBasis(R),
GradedHopfAlgebras(R),
HopfAlgebrasWithBasis(R)
]