Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras

Abstract

We construct a new family of quasigraded Lie algebras that admit the Kostant-Adler scheme. They coincide with special quasigraded deformations of twisted subalgebras of the loop algebras. Using them we obtain new hierarchies of integrable equations in partial derivatives which we call “modified” non-Abelian Toda field hierarchies.