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

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

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

Rings and Algebras 2024-10-14 v1 Quantum Algebra

Authors: Peter Goetz , Ellen E. Kirkman , W. Frank Moore , Kent B. Vashaw

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.

Keywords

Artin-Schelter regular algebra dual reflection group Shephard-Todd-Chevalley theorem algebraic geometry dimension four

Cite

@article{arxiv.2410.08959,
  title  = {Some Artin-Schelter Regular Algebras From Dual Reflection Groups and their Geometry},
  author = {Peter Goetz and Ellen E. Kirkman and W. Frank Moore and Kent B. Vashaw},
  journal= {arXiv preprint arXiv:2410.08959},
  year   = {2024}
}

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

Abstract

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