Lax Operator Algebras and Applications to τ-Symmetries for Multilayer Integrable Couplings

The algebraic structures of zero curvature representations are furnished for multilayer integrable couplings associated with matrix spectral problems, both discrete and continuous. key elements a class loop algebras consisting block matrices blocks the same size. As illustrative examples, isospectral non-isospectral corresponding commutator relations their Lax operators computed explicitly in cases Volterra lattice hierarchy AKNS hierarchy, along τ-symmetry algebras.