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.
Kohno, On the holonomy L ie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces , Nagoya Math
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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.