Algebraic Magnetism Invariants of Self-Actions of Diagonalizable Monoid Schemes

TL;DR

This paper introduces a method to compute algebraic magnetism invariants for self-actions of diagonalizable monoid schemes, linking these invariants to minimal generators of associated monoids and their sharpness.

Contribution

It provides a novel approach to compute pure magnets of monoid scheme actions using minimal generators and monoid quotients, revealing new insights into algebraic magnetism.

Findings

Algebraic magnetism detects sharpness of monoids.

Minimal generators characterize the magnet invariants.

Method applies to diagonalizable monoid schemes.

Abstract

We provide a method to compute the pure magnets of the action of a diagonalizable monoid scheme on itself. This is described in terms of minimal generators of the sharp monoid obtained quotienting by the face of invertible elements. In particular, in this example, algebraic magnetism detects sharpness and minimal generators of the monoid modulo invertible elements.