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When does the associated graded Lie algebra of an arrangement group decompose?

Stefan Papadima·Alexander I. Suciu
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Abstract

Let \A be a complex hyperplane arrangement, with fundamental group G and holonomy Lie algebra \H. Suppose \H_3 is a free abelian group of minimum possible rank, given the values the M\"obius function \mu: \L_2\to \Z takes on the rank 2 flats of \A. Then the associated graded Lie algebra of G decomposes (in degrees 2 and higher) as a direct product of free Lie algebras. In particular, the ranks of the lower central series quotients of the group are given by \phi_r(G)=\sum_{X\in \L_2} \phi_r(F_{\mu(X)}), for r\ge 2. We illustrate this new Lower Central Series formula with several families of examples.

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BibTeXRIS

Stefan Papadima, Alexander I. Suciu. 2003-09-19. When does the associated graded Lie algebra of an arrangement group decompose?. https://doi.org/10.4171/cmh/77

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