On the tensor product construction for q-differential algebras

TL;DR

This paper demonstrates that for q not equal to -1, the q-graded tensor product does not maintain the q-differential structure, indicating the absence of a natural tensor product construction for q-differential algebras.

Contribution

It establishes a fundamental limitation in constructing tensor products of q-differential algebras for certain values of q.

Findings

q-graded tensor product fails to preserve q-differential structure for q ≠ -1

No natural tensor product construction exists for q-differential algebras in this case

The result clarifies structural constraints in q-differential algebra theory

Abstract

We show that for $q\not=-1$ the q-graded tensor product fails to preserve the q-differential structure of the product algebra and therefore there is no natural tensor product construction for q-differential algebras.