Aut-stable subspaces of Grassmann algebras

TL;DR

This paper characterizes Aut-stable subspaces and subalgebras within Grassmann algebras, advancing understanding of their structure and implications in algebraic geometry.

Contribution

It provides a complete characterization of Aut-stable subspaces and subalgebras in Grassmann algebras, extending prior work on polynomial rings.

Findings

All Aut-stable subspaces of Grassmann algebras are characterized.

Aut-stable subalgebras of Grassmann algebras are fully described.

Results contrast with polynomial rings in more than two variables.

Abstract

Recently, the concept of Aut-stable subspaces has played an important role in the characterization of polynomial rings, a topic that remains a challenging problem in algebraic geometry (see [8]). It turns out that polynomial rings with more than two variables do not have any Aut-stable subspaces over an algebraically closed field of characteristic zero [7]. In this work, we characterize all Aut-stable subspaces and Aut-stable subalgebras of Grassmann algebras.