Differential identities of the Grassmann algebra

Abstract

Let F be a field of characteristic zero and let E be the Grassmann algebra of an infinite-dimensional F-vector space. We consider a class of solvable nonabelian finite-dimensional Lie algebras acting on E by derivations, and completely describe the differential polynomial identities satisfied by E. The corresponding $S_n$-cocharacter and differential codimension sequences are computed. Finally, we prove that the differential exponent exists and equals the ordinary exponent of E.