Graded deformations of skew group algebras for cyclic transvection groups acting on polynomial rings in positive characteristic

Fuente: arXiv
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Hauptverfasser: Grimley, Lauren, Krawzik, Naomi, Lawson, Colin M., Uhl, Christine
Format: Preprint
Veröffentlicht: 2024
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author Grimley, Lauren
Krawzik, Naomi
Lawson, Colin M.
Uhl, Christine
author_facet Grimley, Lauren
Krawzik, Naomi
Lawson, Colin M.
Uhl, Christine
contents We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both the group action and the vector space multiplication. We fully characterize the Poincare-Birkhoff-Witt deformations which arise in this setting from multiple perspectives: a necessary and sufficient condition list, a practical road map from which one can generate examples corresponding to any choice of group algebra element, an explicit formula, and a combinatorial analysis of the class of algebras.
format Preprint
id arxiv_https___arxiv_org_abs_2411_05181
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Graded deformations of skew group algebras for cyclic transvection groups acting on polynomial rings in positive characteristic
Grimley, Lauren
Krawzik, Naomi
Lawson, Colin M.
Uhl, Christine
Rings and Algebras
2020: 16E40, 16S35, 16E05, 16E30, 20C20, 20C08
We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both the group action and the vector space multiplication. We fully characterize the Poincare-Birkhoff-Witt deformations which arise in this setting from multiple perspectives: a necessary and sufficient condition list, a practical road map from which one can generate examples corresponding to any choice of group algebra element, an explicit formula, and a combinatorial analysis of the class of algebras.
title Graded deformations of skew group algebras for cyclic transvection groups acting on polynomial rings in positive characteristic
topic Rings and Algebras
2020: 16E40, 16S35, 16E05, 16E30, 20C20, 20C08
url https://arxiv.org/abs/2411.05181