Modules over Fomin-Kirillov algebras and their subalgebras

TL;DR

This paper investigates the structure of modules over Fomin-Kirillov algebras and their subalgebras, providing bounds on truncated point modules and analyzing their geometric properties related to certain graphs.

Contribution

It introduces bounds on the degrees of truncated point modules over generalized Fomin-Kirillov algebras associated with trees and computes truncated point schemes for subalgebras linked to specific graphs.

Findings

Fomin-Kirillov algebras do not admit truncated point modules

Established tight bounds on degrees of truncated point modules for certain subalgebras

Computed truncated point schemes for subalgebras related to specific graphs

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.