Z2-gradings of the Grassmann algebra: construction, PI-equivalence, isomorphisms
Grassmann algebra; Z2-gradings; Automorphisms
The focus of our dissertation is to develope a study on the Z2-gradings of the infinite-
dimensional Grassmann algebra E. The homogeneous Z2-gradings and their Z2-grade identities
are already well known in the literature, see (VINCENZO; SILVA, 2009), (CENTRONE, 2011) and
(GONÇALVES, 2018). Nevertheless, the construction of non-homogeneous Z2-gradings
demands the use of the duality between these structures and automorphisms of order ≤ 2
acting on E. Through this, we will study the non-homogeneous Z2-gradings, producing results
on their construction. In a second moment, we will investigate under what conditions a non-
homogeneous Z2-grading is isomorphic to the canonical Z2-grading of E. Finally, we will
provide a Z2-grading on E in which there is no non-zero element of the space L homogeneous,
refuting the conjecture presented in (GUIMARÃES; KOSHLUKOV, 2023).