### 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 language | English |
---|---|

Pages (from-to) | 1027-1047 |

Number of pages | 21 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 71 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2019 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Solomon–Terao algebra of hyperplane arrangements'. Together they form a unique fingerprint.

## Cite this

*Journal of the Mathematical Society of Japan*,

*71*(4), 1027-1047. https://doi.org/10.2969/jmsj/79957995