Automorphisms and superalgebra structures on the Grassmann algebra

Let F be a field of characteristic zero and let E the Grassmann algebra an infinite dimensional F-vector space L. In this paper we study superalgebra structures (that is Z2-gradings) that admits. By using duality between superalgebras automorphisms order at most 2 prove in many cases Z2-graded polynomial identities for such coincide with “typical” E?, Ek? Ek where vector L homogeneous. Recall these were completely described by Di Vincenzo da Silva [13]. Moreover exhibit wide range non-homogeneous Z2-gradings on are Z2-isomorphic to Ek. particular construct Z2-grading only one homogeneous generator which natural E, here denoted Ecan.