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We represent the coordinate ring of algebraic hulls (which are the fundamental groups of generalizations of the Malcev completions of nilpotent groups for solvable groups) of solvmanifolds /Γ by using Miller’s exponential iterated integrals (which are extensions of Chen’s iterated integrals) of invariant differential forms.

Algebraic hulls of solvable groups and exponential iterated integrals on solvmanifolds