Linearization of skew-periodic loops and $\mathbb S^1$-cocycles

TL;DR

This paper explores the linearization of skew-periodic loops, extending the concept to non-commutative loops and $ ext{S}^1$-cocycles, providing a broader framework for understanding these mathematical structures.

Contribution

It introduces a generalized approach to linearizing skew-periodic loops, including non-commutative cases and $ ext{S}^1$-cocycles, expanding existing theories.

Findings

Established a method for linearizing skew-periodic loops.

Extended linearization techniques to non-commutative loops.

Applied the framework to $ ext{S}^1$-cocycles.

Abstract

We discuss linearization of skew-periodic loops. We generalize the situation to linearization of non-commutative loops and $\mathbb S^1$-cocycles.