On the group aspects of Riemann–Hilbert transformations.

The more general algebraic structures of two-dimensional integrable systems are derived in a model independent manner by using the infinitesimal Riemann–Hilbert transformation. It is found that the resulting algebra decomposes into many families and, for each family, there is a Lie multialgebra structure. Examples of the chiral sigma models, four-dimensional self-dual Yang–Mills field, sine–Gordon, and Liouville equations and the BZ gravity are given with two special Lie products equipped therein. [ABSTRACT FROM AUTHOR]