Realization of graded-simple algebras as loop algebras
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Multiloop algebras determined by $n$ commuting algebra automorphisms of finite order are natural generalizations of the classical loop algebras that are used to realize affine Kac-Moody Lie algebras. In this paper, we obtain necessary and sufficient conditions for a $Z^n$-graded algebra to be realized as a multiloop algebra based on a finite dimensional simple algebra over an algebraically closed field of characteristic 0. We also obtain necessary and sufficient conditions for two such multiloop algebras to be graded-isomorphic, up to automorphism of the grading group.
We prove these facts as consequences of corresponding results for a generalization of the multiloop construction. This more general setting allows us to work naturally and conveniently with arbitrary grading groups and arbitrary base fields.
31 pages. Corrected typos and added minor clarifications. Accepted in Forum Mathematicum
31 pages. Corrected typos and added minor clarifications. Accepted in Forum Mathematicum