Universal lifts of chain complexes over non-commutative parameter algebras

TL;DR

This paper introduces the concept of universal lifts for projective complexes over non-commutative parameter algebras, establishing their existence, uniqueness, and exploring their properties.

Contribution

It defines universal lifts in a non-commutative setting and proves their fundamental existence and uniqueness, advancing the understanding of parameter algebras.

Findings

Universal lifts exist and are unique for projective complexes.

Properties of parameter algebras for universal lifts are characterized.

The framework extends classical lift concepts to non-commutative contexts.

Abstract

We define the notion of universal lift of a projective complex based on non-commutative parameter algebras, and prove its existence and uniqueness. We investigate the properties of parameter algebras for universal lifts.