Colin M. Lawson | Searcharxiv

arXiv2026

Deformation cohomology for cyclic groups acting on polynomial rings

We examine the Hochschild cohomology governing graded deformations for finite cyclic groups acting on polynomial rings. We classify the infinitesimal graded deformations of the skew group algebra $S\rtimes G$ for a cyclic group $G$ acting on a polynomial ring $S$. This gives all graded deformations of the first order. We are particularly interested in the case when the characteristic of the underlying field divides the order of the acting group, which complicates the determination of cohomology.

math.RA↗

arXiv2024

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

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.

math.RA↗