A classification of generalized root systems

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  • Justus Liebig University Giessen
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Original languageEnglish
Pages (from-to)567–583
Number of pages17
JournalArchiv der Mathematik
Volume123
Issue number6
Early online date1 Oct 2024
Publication statusPublished - Dec 2024

Abstract

Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture that every generalized root system is equivalent to one associated to a restriction of a Weyl arrangement. In this note we prove the conjecture and provide a complete classification of generalized root systems up to equivalence.

Keywords

    16T30, 17B22, 52C35, Algebraic groups, Root system, Weyl group

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Cite this

A classification of generalized root systems. / Cuntz, Michael; Mühlherr, B.
In: Archiv der Mathematik, Vol. 123, No. 6, 12.2024, p. 567–583.

Research output: Contribution to journalArticleResearchpeer review

Cuntz M, Mühlherr B. A classification of generalized root systems. Archiv der Mathematik. 2024 Dec;123(6):567–583. Epub 2024 Oct 1. doi: 10.1007/s00013-024-02046-1, 10.48550/arXiv.2404.00278
Cuntz, Michael ; Mühlherr, B. / A classification of generalized root systems. In: Archiv der Mathematik. 2024 ; Vol. 123, No. 6. pp. 567–583.
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