A basis construction of the extended Catalan and Shi arrangements of the type A2

Takuro Abe, Daisuke Suyama

Research output: Contribution to journalArticle

Abstract

In [10], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method, Yoshinaga proved the freeness of the extended Catalan or Shi arrangements in [12]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements. In this paper, we give the first explicit construction of them when the root system is of the type A2.

Original languageEnglish
Pages (from-to)20-35
Number of pages16
JournalJournal of Algebra
Volume493
DOIs
Publication statusPublished - Jan 1 2018

Fingerprint

Arrangement
Root System
Multiplicity
Logarithmic
Module

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

A basis construction of the extended Catalan and Shi arrangements of the type A2 . / Abe, Takuro; Suyama, Daisuke.

In: Journal of Algebra, Vol. 493, 01.01.2018, p. 20-35.

Research output: Contribution to journalArticle

@article{140138015acd49d693a6eaf266ff2e57,
title = "A basis construction of the extended Catalan and Shi arrangements of the type A2",
abstract = "In [10], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method, Yoshinaga proved the freeness of the extended Catalan or Shi arrangements in [12]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements. In this paper, we give the first explicit construction of them when the root system is of the type A2.",
author = "Takuro Abe and Daisuke Suyama",
year = "2018",
month = "1",
day = "1",
doi = "10.1016/j.jalgebra.2017.09.024",
language = "English",
volume = "493",
pages = "20--35",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - A basis construction of the extended Catalan and Shi arrangements of the type A2

AU - Abe, Takuro

AU - Suyama, Daisuke

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In [10], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method, Yoshinaga proved the freeness of the extended Catalan or Shi arrangements in [12]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements. In this paper, we give the first explicit construction of them when the root system is of the type A2.

AB - In [10], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method, Yoshinaga proved the freeness of the extended Catalan or Shi arrangements in [12]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements. In this paper, we give the first explicit construction of them when the root system is of the type A2.

UR - http://www.scopus.com/inward/record.url?scp=85042160666&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042160666&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.09.024

DO - 10.1016/j.jalgebra.2017.09.024

M3 - Article

VL - 493

SP - 20

EP - 35

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -