• Corpus ID: 8740027

Centralizers of Lie Algebras Associated to the Descending Central Series of Certain Poly-Free Groups

@article{Cohen2006CentralizersOL,
  title={Centralizers of Lie Algebras Associated to the Descending Central Series of Certain Poly-Free Groups},
  author={Daniel C. Cohen and Frederick R. Cohen and Stratos Prassidis},
  journal={arXiv: Group Theory},
  year={2006}
}
Poly-free groups are constructed as iterated semidirect products of free groups. The class of poly-free groups includes the classical pure braid groups, fundamental groups of fiber-type hyperplane arrangements, and certain subgroups of the automorphism groups of free groups. The purpose of this article is to compute centralizers of certain natural Lie subalgebras of the Lie algebra obtained from the descending central series of poly-free groups G including some of the geometrically interesting… 

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References

SHOWING 1-10 OF 34 REFERENCES

Homology of iterated semidirect products of free groups

Basis-conjugating automorphisms of a free group and associated Lie algebras

Let F_n = denote the free group with generators {x_1,...,x_n}. Nielsen and Magnus described generators for the kernel of the canonical epimorphism from the automorphism group of F_n to the general

On injective homomorphisms for pure braid groups, and associated Lie algebras

Monodromy of fiber-type arrangements and orbit configuration spaces

We prove similar theorems concerning the structure of bundles involving complements of fiber-type hyperplane arrangements and orbit configuration spaces. These results facilitate analysis of the

LIE ALGEBRAS ASSOCIATED TO FIBER-TYPE ARRANGEMENTS

Given a hyperplane arrangement in a complex vector space of dimen- sion ', there is a natural associated arrangement of codimension k subspaces in a complex vector space of dimension k'. Topological

On Basis-Conjugating Automorphisms of Free Groups

  • J. McCool
  • Mathematics
    Canadian Journal of Mathematics
  • 1986
Let X = {x 1, … xn } be a free generating set of the free group Fn and let H be the subgroup of Aut Fn consisting of those automorphisms α such that α(xi ) is conjugate to xi for each i = 1, 2 , …,

On the linearity problem for mapping class groups

Formanek and Procesi have demonstrated that Aut(Fn) is not linear for n 3. Their technique is to construct nonlinear groups of a special form, which we call FP-groups, and then to embed a special

ARTIN'S BRAID GROUPS, FREE GROUPS, AND THE LOOP SPACE OF THE 2-SPHERE

The purpose of this article is to describe a connection between the single loop space of the 2-sphere, Artin’s braid groups, a choice of simplicial group whose homotopy groups are given by modules

The integral cohomology of the group of loops

Let PSigma_n denote the group that can be thought of either as the group of motions of the trivial n-component link or the group of symmetric automorphisms of a free group of rank n. The integral