THE CENTRAL POLYNOMIALS FOR THE GRASSMANN ALGEBRA

In this paper we describe the central polynomials for the infinite-dimensional unitary Grassmann algebra G over an infinite field F of characteristic not equal 2. We exhibit a set of polynomials that generates the vector space C( G) of the central polynomials of G as a T-space. Using a deep result of Shchigolev we prove that if char F = p > 2 then the T-space C( G) is not finitely generated. Moreover, over such a field F, C( G) is a limit T-space, that is, C( G) is not a finitely generated T-space but every larger T-space W not greater than or equal to C( G) is. We obtain similar results for the infinite-dimensional non-unitary Grassmann algebra H as well.