Algebraic hulls of solvable groups and exponential iterated integrals on solvmanifolds

Abstract: We represent the coordinate ring of algebraic hulls (which are generalizations of the Malcev completions of nilpotent groups for solvable groups) of solvmanifolds $G/\Gamma$ by using Miller's exponential iterated integrals (which are extensions of Chen's iterated integrals) of invariant differential forms.