Recursively free reflection arrangements

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Authors

  • Paul Mücksch

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Details

Original languageEnglish
Pages (from-to)24-48
Number of pages25
JournalJournal of Algebra
Volume474
Issue number474
Publication statusPublished - 15 Mar 2017

Abstract

Let A=A(W) be the reflection arrangement of the finite complex reflection group $W$. By Terao's famous theorem, the arrangement A is free. In this paper we classify all reflection arrangements which belong to the smaller class of recursively free arrangements. Moreover for the case that W admits an irreducible factor isomorphic to G_{31} we obtain a new (computer-free) proof for the non-inductive freeness of A(W). Since our classification implies the non-recursive freeness of the reflection arrangement A(G_{31}), we can prove a conjecture by Abe about the new class of divisionally free arrangements which he recently introduced.

Keywords

    Divisionally free arrangements, Hyperplane arrangements, Inductively free arrangements, Recursively free arrangements, Reflection arrangements

ASJC Scopus subject areas

Cite this

Recursively free reflection arrangements. / Mücksch, Paul.
In: Journal of Algebra, Vol. 474, No. 474, 15.03.2017, p. 24-48.

Research output: Contribution to journal › Article › Research › peer review

Mücksch P. Recursively free reflection arrangements. Journal of Algebra. 2017 Mar 15;474(474):24-48. doi: 10.1016/j.jalgebra.2016.10.041
Mücksch, Paul. / Recursively free reflection arrangements. In: Journal of Algebra. 2017 ; Vol. 474, No. 474. pp. 24-48.
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