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central idempotent of a finite dimensional algebra

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative() B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]), Matrix([[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0]]), Matrix([[0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,1,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,0]]), Matrix([[0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0]]), Matrix([[0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0]]), Matrix([[0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0]]), Matrix([[0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1]])], category=A) B.central_orthogonal_idempotents()

The above code gives me error. Could anyone tell me how to fix the code?

central idempotent of a finite dimensional algebra

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative() A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative()

B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]), Matrix([[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0]]), Matrix([[0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,1,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,0]]), Matrix([[0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0]]), Matrix([[0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0]]), Matrix([[0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0]]), Matrix([[0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1]])], category=A) category=A)

B.central_orthogonal_idempotents()

The above code gives me error. Could anyone tell me how to fix the code?enter code here

click to hide/show revision 3
None

central idempotent of a finite dimensional algebra

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative()

B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]), Matrix([[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0]]), Matrix([[0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,1,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,0]]), Matrix([[0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0]]), Matrix([[0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0]]), Matrix([[0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0]]), Matrix([[0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1]])], category=A)

category=A)

B.central_orthogonal_idempotents()

B.central_orthogonal_idempotents()

The above code gives me error. Could anyone tell me how to fix the code?enter code here

click to hide/show revision 4
None

central idempotent of a finite dimensional algebra

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative()

B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]), Matrix([[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0]]), Matrix([[0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,1,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,0]]), Matrix([[0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0]]), Matrix([[0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0]]), Matrix([[0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0]]), Matrix([[0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1]])], category=A)

B.central_orthogonal_idempotents()

The above code gives me error. Could anyone tell me how to fix the code?enter code here

click to hide/show revision 5
None

central idempotent of a finite dimensional algebra

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative()

B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0],  [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]), Matrix([[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0]]), Matrix([[0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,1,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,0]]), Matrix([[0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0]]), Matrix([[0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0]]), Matrix([[0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0]]), Matrix([[0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1]])], category=A)

B.central_orthogonal_idempotents()

The above code gives me error. Could anyone tell me how to fix the code?enter code here

click to hide/show revision 6
None

central idempotent of a finite dimensional algebra

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative()

B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], 
[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]), Matrix([[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0]]), Matrix([[0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,1,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,0]]), Matrix([[0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0]]), Matrix([[0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0]]), Matrix([[0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0]]), Matrix([[0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1]])], category=A)

B.central_orthogonal_idempotents()

The above code gives me error. Could anyone tell me how to fix the code?enter code here

click to hide/show revision 7
None

central idempotent of a finite dimensional algebra

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative()I tried the following

A=Algebras(QQ).FiniteDimensional().WithBasis().Semisimple().Commutative()

B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], 
[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]), Matrix([[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0]]), Matrix([[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0]]), Matrix([[0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,1,0,0,0,0,1,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,1,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,0]]), Matrix([[0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0]]), Matrix([[0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0]]), Matrix([[0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,2,0,0,0,2,0,0,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [2,0,0,0,2,0,0,0,1], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0]]), Matrix([[0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,2,2,0,0,0,0,0], [2,0,0,0,2,0,0,0,0], [0,2,0,0,0,2,0,0,0], [0,2,0,0,0,2,1,0,0], [0,0,2,2,0,0,0,1,0], [2,0,0,0,2,0,0,0,1]])], category=A)

B.central_orthogonal_idempotents()

The above code gives me error. Could anyone tell me how to fix the code?enter code here