Universal suspension via Non-commutative motives

TL;DR

This paper develops a universal suspension model for non-commutative motives using infinite matrices, which applies broadly across various classical invariants like K-theory and Hochschild homology.

Contribution

It introduces a simple, matrix-based model for suspension in non-commutative motives that works universally across multiple invariants.

Findings

Model applies to all classical invariants such as Hochschild and cyclic homology.

Provides a unified framework for suspension in non-commutative motives.

Simplifies computations in non-commutative geometry.

Abstract

In this article we further the study of non-commutative motives. Our main result is the construction of a simple model, given in terms of infinite matrices, for the suspension in the triangulated category of non-commutative motives. As a consequence, this simple model holds in all the classical invariants such as Hochschild homology, cyclic homology and its variants (periodic, negative, ...), algebraic K-theory, topological Hochschild homology, topological cyclic homology, ...