Bases: sage.categories.category_with_axiom.CategoryWithAxiom_over_base_ring
The category of finite dimensional algebras with a distinguished basis.
EXAMPLES:
sage: C = FiniteDimensionalAlgebrasWithBasis(QQ); C
Category of finite dimensional algebras with basis over Rational Field
sage: C.super_categories()
[Category of algebras with basis over Rational Field,
Category of finite dimensional modules with basis over Rational Field]
TESTS:
sage: TestSuite(C).run()
sage: C is Algebras(QQ).FiniteDimensional().WithBasis()
True
sage: C is Algebras(QQ).WithBasis().FiniteDimensional()
True
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