Classification of Reductive Monoid Spaces Over an Arbitrary Field

TL;DR

This paper reviews spherical spaces and presents recent classification results over arbitrary fields, culminating in the introduction and classification of reductive monoid spaces, expanding understanding of algebraic monoid structures.

Contribution

It provides a comprehensive review of spherical spaces and introduces a new classification of reductive monoid spaces over arbitrary fields, extending previous work.

Findings

Classification of spherical spaces over arbitrary fields

Introduction of reductive monoid spaces over arbitrary fields

New classification results for algebraic monoid structures

Abstract

In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify reductive monoid spaces over an arbitrary field.