Graded-simple algebras and cocycle twisted loop algebras

TL;DR

This paper extends the theory of graded-central-simple algebras by removing centroid restrictions and introducing cocycle twists, broadening the class of loop algebras that can be described.

Contribution

It generalizes the loop algebra construction to include cocycle twists, removing previous centroid restrictions.

Findings

Extended the classification of graded-simple algebras

Introduced cocycle twists to loop algebra construction

Broadened the scope of algebraic structures covered

Abstract

The loop algebra construction by Allison, Berman, Faulkner, and Pianzola, describes graded-central-simple algebras with split centroid in terms of central simple algebras graded by a quotient of the original grading group. Here the restriction on the centroid is removed, at the expense of allowing some deformations (cocycle twists) of the loop algebras.