  In this article the holonomy-flux *-algebra, which has been introduced by
Lewandowski, Okolow, Sahlmann and Thiemann, is modificated. The new *-algebra
is called the holonomy-flux cross-product *-algebra. This algebra is an
abstract cross-product *-algebra. It is given by the universal algebra of the
algebra of continuous and differentiable functions on the configuration space
of generalised connections and the universal enveloping flux algebra associated
to a surface set, and some canonical commutator relations. There is a
uniqueness result for a certain path- and graph-diffeomorphism invariant state
of the holonomy-flux cross-product *-algebra. This new *-algebra is not the
only *-algebra, which is generated by the algebra of certain continuous and
differentiable functions on the configuration space of generalised connections
and the universal enveloping flux algebra associated to a surface set. The
theory of abstract cross-product algebras allows to define different new
*-algebras. Some of these algebras are presented in this article.
