Some Artin-Schelter Regular Algebras From Dual Reflection Groups and their Geometry

2024/10/11 by Goetz, Peter, Kirkman, Ellen E., Moore, W. Frank +1 · 1 citation
#16E65 #16S37 #16S38 #16T05 #16W22 #16W50 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2410.08959

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.

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• Some components of the moduli space of Koszul Artin-Schelter regular algebras of dimension four

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