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Modules over Fomin-Kirillov algebras and their subalgebras

Be'eri Greenfeld, Sarah Mathison, Aditya Saini, Scott Wynn

Abstract

We compute the truncated point schemes of subalgebras of Fomin-Kirillov algebras associated with certain graphs. While Fomin-Kirillov algebras do not admit any truncated point modules, we prove a tight bound on the degrees of truncated point modules over generalized Fomin-Kirillov algebras associated with trees.

Modules over Fomin-Kirillov algebras and their subalgebras

Abstract

We compute the truncated point schemes of subalgebras of Fomin-Kirillov algebras associated with certain graphs. While Fomin-Kirillov algebras do not admit any truncated point modules, we prove a tight bound on the degrees of truncated point modules over generalized Fomin-Kirillov algebras associated with trees.

Paper Structure

This paper contains 3 sections, 7 theorems, 24 equations.

Table of Contents

  1. Introduction
  2. Modules over Fomin-Kirillov algebras
  3. Generalized Fomin-Kirillov Algebras

Key Result

Theorem 1.1

Let $n\geq 3$ be an integer. Then $\mathcal{E}_n$ admits no truncated point modules of degree greater than $1$.

Theorems & Definitions (14)

  • Theorem 1.1
  • Theorem 1.2
  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • proof : Proof of Theorem \ref{['thm:fk']}
  • Corollary 3.1
  • proof
  • Proposition 3.2
  • ...and 4 more