graded tensor product

If A and B are -graded algebrasMathworldPlanetmath, we define the graded tensor product (or super tensor product) AsuB to be the ordinary tensor productPlanetmathPlanetmath as graded modulesMathworldPlanetmath, but with multiplication - called the super productPlanetmathPlanetmath - defined by

(ab)(ab)=(-1)(deg b)(deg a)aabb

where a,a,b,b are homogeneousPlanetmathPlanetmathPlanetmath. The super tensor product of A and B is itself a graded algebra, as we grade the super tensor product of A and B as follows:

(AsuB)n=p,q : p+q=nApBq
Title graded tensor product
Canonical name GradedTensorProduct
Date of creation 2013-03-22 12:45:44
Last modified on 2013-03-22 12:45:44
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 8
Author mathcam (2727)
Entry type Definition
Classification msc 16W55
Related topic TensorProduct
Defines super tensor product