Abstract: Given an arrangement of complex hyperplanes, there are several graded Lie algebras naturally attached to it:
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the holonomy Lie algebra of the cohomology ring;
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the associated graded Lie algebra of the fundamental group;
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the Chen Lie algebra of the fundamental group;
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the homotopy Lie algebra of the cohomology ring;
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the homotopy Lie algebra of the ``redundant" subspace arrangement.
In this talk, I will define these objects (in greater generality), indicate some relations among them, and sketch ways to compute their graded ranks, under certain assumptions.
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