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

Graded-simple algebras and cocycle twisted loop algebras