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AssociativeAlgebras :: qTensorProduct

qTensorProduct -- Define the (q-)commuting tensor product

Synopsis

Description

This function returns the algebra that contains A and B as a subalgebra, with the commutation law on the images of A and B given by a*b = q*b*a for all a in A and b in B. In the case of A ** B, q = 1.

i1 : A = QQ<|x,y|>

o1 = A

o1 : FreeAlgebra
i2 : B = skewPolynomialRing(QQ,(-1)_QQ, {a,b})

o2 = B

o2 : FreeAlgebraQuotient
i3 : C = qTensorProduct(A,B,-1_QQ)

o3 = C

o3 : FreeAlgebraQuotient
i4 : ideal C

o4 = ideal (a*b + b*a, x*a + a*x, x*b + b*x, y*a + a*y, y*b + b*y)

o4 : Ideal of QQ <|x, y, a, b|>
i5 : D = A ** B

o5 = D

o5 : FreeAlgebraQuotient
i6 : ideal D

o6 = ideal (a*b + b*a, - x*a + a*x, - x*b + b*x, - y*a + a*y, - y*b + b*y)

o6 : Ideal of QQ <|x, y, a, b|>

Ways to use qTensorProduct :

For the programmer

The object qTensorProduct is a method function.