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Separating invariants and finite reflection groups

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JournalAdvances in Mathematics
DatePublished - 20 Aug 2009
Issue number6
Volume221
Number of pages11
Pages (from-to)1979-1989
Original languageEnglish

Abstract

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras.

    Research areas

  • Bireflections, Complete intersection ring, Finite groups, Invariant theory, Polynomial ring, Reflections, Separating invariants

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