Solomon–Terao algebra of hyperplane arrangements

Takuro Abe, Toshiaki Maeno, Satoshi Murai, Yasuhide Numata

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We introduce a new algebra associated with a hyperplane arrangement A, called the Solomon–Terao algebra ST(A, η), where η is a homogeneous polynomial. It is shown by Solomon and Terao that ST(A, η) is Artinian when η is generic. This algebra can be considered as a generalization of coinvariant algebras in the setting of hyperplane arrangements. The class of Solomon–Terao algebras contains cohomology rings of regular nilpotent Hessenberg varieties. We show that ST(A, η) is a complete intersection if and only if A is free. We also give a factorization formula of the Hilbert polynomials of ST(A, η) when A is free, and pose several related questions, problems and conjectures.

Original languageEnglish
Pages (from-to)1027-1047
Number of pages21
JournalJournal of the Mathematical Society of Japan
Volume71
Issue number4
DOIs
Publication statusPublished - 2019

Keywords

  • Artinian ring
  • Complete intersection ring
  • Free arrangements
  • Hyperplane arrangements
  • Logarithmic derivation modules
  • Solomon–Terao formula

ASJC Scopus subject areas

  • Mathematics(all)

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