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The expansion method of Lie algebras by a semigroup or S-expansion isgeneralized to act directly on the group manifold, and not only at the level ofits Lie algebra. The consistency of this generalization with the dualformulation of the S-expansion is also verified. This is used to show that theLie algebras of smooth mappings of some manifold M onto a finite-dimensionalLie algebra, such as the so called loop algebras, can be interpreted as aparticular kind of S-expanded Lie algebras. We consider as an example theconstruction of a Yang-Mills theory for an infinite-dimensional algebra, namelyloop algebra.

Lie Group S-Expansions and Infinite-dimensional Lie algebras