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

2009/10/20 by Dubois-Violette, Michel
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0910.3817

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.

Related

• On the tensor product construction for q-differential algebras
• Structures on the Category of N-Complexes
• Differential calculus over N-graded commutative rings
• Types of graded tensor products of graded von Neumann algebras
• Noncommutative Galois Extension and Graded q-Differential Algebra