The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.

In this paper, first we introduce the notions of relative Rota-Baxter operators nonzero weight on $3$-Lie algebras and $3$-post-Lie algebras. A 3-post-Lie algebra consists a 3-Lie structure ternary operation such that some compatibility conditions are satisfied. We show operator induces naturally. Conversely, gives rise to new algebra, which is called subadjacent an action original algebra. The...

The goal of this work is to introduce the notion 3-Hom-L-dendriform algebras which dendriform version 3-Hom-Lie-algebras. They can be also regarded as ternary analogous Hom-L-de...

Local commuting charges in sigma-models with classical Lie groups as target manifolds are shown to be related to the conserved quantities appearing in the DrinfeldSokolov (generalized mKdV) hierarchies. Conversely, the Drinfeld-Sokolov construction can be used to deduce the existence of commuting charges in these and in wider classes of sigma-models, including those whose target manifolds are e...

After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.

For the symmetric space sigma model in the internal metric formalism we explicitly construct the lagrangian in terms of the axions and the dilatons of the solvable Lie algebra gauge and then we exactly derive the axion-dilaton field equations.