For fiber-type and hypersolvable arrangements, the holonomy Lie algebra is an iterated almost-direct product of free Lie algebras with ranks equal to the arrangement exponents.
Chen, Iterated integrals of differential forms and loop space homology , Ann
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Holonomy Lie algebra of a geometric lattice
For fiber-type and hypersolvable arrangements, the holonomy Lie algebra is an iterated almost-direct product of free Lie algebras with ranks equal to the arrangement exponents.