Lie Group S-Expansions and Infinite-dimensional Lie algebras

Details Lie Group S-Expansions and Infinite-dimensional Lie algebras Lie Group S-Expansions and Infinite-dimensional Lie algebras

2010-05-04

arxiv.org/abs/1005.0495v2

Physics

High Energy Physics

High Energy Physics - Theory

minor correction, references added

Scientific paper

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

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