Some Artin–Schelter regular algebras from dual reflection groups and their geometry

Peter Goetz; Ellen Kirkman; W. Frank Moore; Kent Vashaw

doi:10.4171/jncg/658

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Some Artin–Schelter regular algebras from dual reflection groups and their geometry

Peter Goetz
California State Polytechnic University, Humboldt, Arcata, USA
Ellen Kirkman
Wake Forest University, Winston-Salem, USA
W. Frank Moore
Wake Forest University, Winston-Salem, USA
Kent Vashaw
University of California, Los Angeles, USA

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Abstract

Let $G$ be a group coacting on an Artin–Schelter regular algebra $A$ homogeneously and inner faithfully. When the identity component $A_{e}$ is also Artin–Schelter regular, providing a generalization of the Shephard–Todd–Chevalley theorem, we say that $G$ is a dual reflection group for $A$ . We give two examples of dual reflection groups of order $16$ and study algebraic and geometric properties of three associated Artin–Schelter regular algebras of dimension four.

Cite this article

Peter Goetz, Ellen Kirkman, W. Frank Moore, Kent Vashaw, Some Artin–Schelter regular algebras from dual reflection groups and their geometry. J. Noncommut. Geom. (2026), published online first

DOI 10.4171/JNCG/658