Solomon–Terao algebra of hyperplane arrangements
| Autor: | Takuro Abe, Satoshi Murai, Yasuhide Numata, Toshiaki Maeno |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
Complete intersection Solomon–Terao formula logarithmic derivation modules 01 natural sciences free arrangements Factorization 0103 physical sciences 0101 mathematics Nuclear Experiment Mathematics complete intersection ring 13E10 Mathematics::Commutative Algebra 010102 general mathematics Artinian ring Complete intersection ring Cohomology Algebra Nilpotent Homogeneous polynomial hyperplane arrangements 010307 mathematical physics Hessenberg variety 32S22 |
| Zdroj: | J. Math. Soc. Japan 71, no. 4 (2019), 1027-1047 |
| Popis: | We introduce a new algebra associated with a hyperplane arrangement $\mathcal{A}$, called the Solomon–Terao algebra $ST(\mathcal{A}, \eta)$, where $\eta$ is a homogeneous polynomial. It is shown by Solomon and Terao that $ST(\mathcal{A}, \eta)$ is Artinian when $\eta$ 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 $ST(\mathcal{A}, \eta)$ is a complete intersection if and only if $\mathcal{A}$ is free. We also give a factorization formula of the Hilbert polynomials of $ST(\mathcal{A}, \eta)$ when $\mathcal{A}$ is free, and pose several related questions, problems and conjectures. |
| Databáze: | OpenAIRE |
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