Descrição: In this paper we present a general framework to construct integrable $\Z2$-graded extensions of classical, two-dimensional Toda and conformal affine Toda theories. The scheme is applied to define the extended Liouville and Sinh-Gordon models; they are based on $\Z2$-graded color Lie algebras and their fields satisfy a parabosonic statistics. The mathematical tools here introduced are the $\Z2$-graded covariant extensions of the Lax pair formalism and of the Polyakov's soldering procedure. The $\Z2$-graded Sinh-Gordon model is derived from an affine $\Z2$-graded color Lie algebra, mimicking a procedure originally introduced by Babelon-Bonora to derive the ordinary Sinh-Gordon model. The color Lie algebras under considerations are: the $6$-generator $\Z2$-graded $sl_2$, the $\Z2$-graded affine ${\widehat{sl_2}}$ algebra with two central extensions, the $\Z2$-graded Virasoro algebra obtained from a Hamiltonian reduction.

Número: CBPF-NF-005/24