ℤ₂-Graded Gelfand–Kirillov dimension of the Grassmann algebra

Abstract

We consider the infinite dimensional Grassmann algebra E over a field F of characteristic 0 or p, where p > 2, and we compute its Z 2 -graded Gelfand-Kirillov (GK) dimension as a Z 2 -graded PI-algebra.

On the Z_2-graded codimensions of the Grassmann algebra over a finite field

“…The previous result gives us that the Z 2 -graded Gelfand-Kirillov dimension of E in a fixed number of graded variables is 0. See [4] for more details about the graded Gelfand-Kirillov dimension of graded algebras and [3] for a comparison with the case of E over an infinite field. Now we start to focus on codimensions.…”

“…Due to its prominent role in the Kemer's theory about the structure of T -ideals (see [10]) and its own interest, the (graded) identities of E have been intensively studied. See for example the works by Krakowski and Regev [11], Regev [13], Giambruno and Koshlukov [9], Anisimov [1], Di Vincenzo and da Silva [5], Centrone [3], Bekh-Ochir [2] and Fonseca [7].…”