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

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: S. Papadima, A. I. Suciu

Editorial: Commentarii Mathematici Helvetici, 81 (4), p.859-875, 2006.

Rezumat:

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 -> 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.

Cuvinte cheie: Hyperplane arrangement, lower central series, associated graded Lie algebra, holonomy Lie algebra, Chen Lie algebra

URL: http://dx.doi.org/10.4171/CMH/77