Infinitesimal algebraic skeletons for a (2+1)-dimensional Toda type system

A tower for a (2+1)-dimensional Toda type system is constructed in terms of a series expansion of operators which can be interpreted as generalized Bessel coefficients; the result is formulated as an analog of the Baker-Campbell-Hausdorff formula. We tackle the problem of the construction of infinitesimal algebraic skeletons for such a tower and discuss some open problems arising along our approach. In particular, we realize the prolongation skeleton as a Kac-Moody algebra.