Aut-stable subspaces of Grassmann algebras

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.