Given a Lie algebra g sitting inside an associative algebra A and any associative algebra F, the F-loop algebra is the Lie subalgebra of tensor product F\otimes A generated by F\otimes g.
For a large class of Lie algebras g, including semisimple ones, there is an explicit description of all F-loop algebras. This description has a striking resemblance to the commutator expansions of F used by M. Kapranov in his approach to noncommutative geometry.
I will also define and study Lie groups associated with F-loop algebras. This is a joint paper with A. Berenstein (Univ. of Oregon).