Tensor product of N-complexes and generalization of graded differential algebras

TL;DR

This paper generalizes graded differential algebras by utilizing the monoidal structure of N-complexes, linking them to graded q-differential algebras, thus broadening the algebraic framework.

Contribution

It introduces a new class of algebras as monoids in the monoidal category of N-complexes, generalizing graded differential algebras.

Findings

Generalization coincides with graded q-differential algebras

Provides a categorical framework for N-complexes

Establishes a connection between monoidal structures and algebraic notions

Abstract

It is known that the notion of graded differential algebra coincides with the notion of monoid in the monoidal category of complexes. By using the monoidal structure introduced by M. Kapranov for the category of $N$-complexes we define the corresponding generalization of graded differential algebras as the monoids of this category. It turns out that this generalization coincides with the notion of graded $q$-differential algebra which has been previously introduced and studied.