The Module Structure of a Group Action on a Ring

Peter Symonds

The Module Structure of a Group Action on a Ring

Commutative Algebra 2024-05-15 v4 Representation Theory

Authors: Peter Symonds

Abstract

Consider a finite group $G$ acting on a graded Noetherian $k$ -algebra $S$ , for some field $k$ of characteristic $p$ ; for example $S$ might be a polynomial ring. Regard $S$ as a $kG$ -module and consider the multiplicity of a particular indecomposable module as a summand in each degree. We show how this can be described in terms of homological algebra and how it is linked to the geometry of the group action on the spectrum of $S$ .

Keywords

module theory partial actions algebraic group actions

Cite

@article{arxiv.2205.03379,
  title  = {The Module Structure of a Group Action on a Ring},
  author = {Peter Symonds},
  journal= {arXiv preprint arXiv:2205.03379},
  year   = {2024}
}

Comments

Rewrote part of section 3 to clarify argument. Corrected calculations of examples in section 9

The Module Structure of a Group Action on a Ring

Abstract

Keywords

Cite

Comments

Related papers