Abstract

Iterated loop algebras are by definition obtained by repeatedly applying the loop construction, familiar from the theory of afine Kac–Moody Lie algebras, to a given base algebra. Our interest in this iterated construction is motivated by its use in the realization of extended afine Lie algebras, but the construction also appears naturally in the study of other classes of algebras. This paper consists of a detailed study of the basic properties of iterated loop algebras.

Keywords

loop algebra, Lie algebra, associative algebra, Jordan algebra

Mathematical Subject Classification

Primary: 17B65

Secondary: 17B67, 16S99, 17C99, 17D05, 17A01

Authors