SOME EXAMPLES OF THE ALGEBRA OF FLOWS

The algebra of the group of smooth maps from a manifold M to a compact simple Lie group G is studied for two cases. The first is when M is the double coset SO(d,R)\SO(d + 1,R)/SO(d,R), the corresponding maps are those from a d sphere to G that are invariant under left translations by elements from SO(d,R). In the second example, M is a two-dimensional torus. The problem of central extension of these algebras is solved. For the first example, no central extension is possible. For the second, the number of independent central extensions is infinite. © 1990 American Institute of Physics.