Bases: sage.categories.category_types.Category_over_base_ring
The category of finite dimensional algebras with a distinguished basis
EXAMPLES:
sage: FiniteDimensionalAlgebrasWithBasis(QQ)
Category of finite dimensional algebras with basis over Rational Field
sage: FiniteDimensionalAlgebrasWithBasis(QQ).super_categories()
[Category of finite dimensional modules with basis over Rational Field, Category of algebras with basis over Rational Field]
TESTS:
sage: TestSuite(FiniteDimensionalAlgebrasWithBasis(ZZ)).run()
Returns the matrix of the action of self on the algebra my multiplication on the left
If new_BR is specified, then the matrix will be over new_BR.
EXAMPLES:
sage: QS3 = SymmetricGroupAlgebra(QQ, 3)
sage: a = QS3([2,1,3])
sage: a.on_left_matrix()
[0 0 1 0 0 0]
[0 0 0 0 1 0]
[1 0 0 0 0 0]
[0 0 0 0 0 1]
[0 1 0 0 0 0]
[0 0 0 1 0 0]
sage: a.on_left_matrix(RDF)
[0.0 0.0 1.0 0.0 0.0 0.0]
[0.0 0.0 0.0 0.0 1.0 0.0]
[1.0 0.0 0.0 0.0 0.0 0.0]
[0.0 0.0 0.0 0.0 0.0 1.0]
[0.0 1.0 0.0 0.0 0.0 0.0]
[0.0 0.0 0.0 1.0 0.0 0.0]
AUTHOR: Mike Hansen
Returns the matrix of the action of self on the algebra my multiplication on the left
If new_BR is specified, then the matrix will be over new_BR.
EXAMPLES:
sage: QS3 = SymmetricGroupAlgebra(QQ, 3)
sage: a = QS3([2,1,3])
sage: a.on_left_matrix()
[0 0 1 0 0 0]
[0 0 0 0 1 0]
[1 0 0 0 0 0]
[0 0 0 0 0 1]
[0 1 0 0 0 0]
[0 0 0 1 0 0]
sage: a.on_left_matrix(RDF)
[0.0 0.0 1.0 0.0 0.0 0.0]
[0.0 0.0 0.0 0.0 1.0 0.0]
[1.0 0.0 0.0 0.0 0.0 0.0]
[0.0 0.0 0.0 0.0 0.0 1.0]
[0.0 1.0 0.0 0.0 0.0 0.0]
[0.0 0.0 0.0 1.0 0.0 0.0]
AUTHOR: Mike Hansen
EXAMPLES:
sage: FiniteDimensionalAlgebrasWithBasis(QQ).super_categories()
[Category of finite dimensional modules with basis over Rational Field, Category of algebras with basis over Rational Field]