Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3234
Abstract
The main purpose of this paper is to provide a survey of results concerning the $\mathbb{Z}$-gradings on the infinite-dimensional Grassmann algebra $E$ over a field of characteristic zero. First, we provide graded identities and central polynomials for $E$ equipped with fine gradings on $E$ by the semigroup $(\mathbb{Z}^\ast,\times)$. We also describe briefly techniques in order to illustrate some important methods to exhibit graded identities and central polynomials of $E$ for other abelian groups. In particular, over a field of characteristic zero, so-called $2$-induced gradings of full support were considered. In order to obtain these descriptions, we strongly use elementary number theory as a tool, providing an interesting connection between this area and PI-Theory.
Keywords
Grassmann algebra, graded identity, graded central polynomial, full support
First Page
1814
Last Page
1827
Recommended Citation
FIDELIS, CLAUDEMIR
(2022)
"$\mathbb{Z}$-graded identities on the infinite-dimensional Grassmann algebra and arithmetic tools: revisited,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 13.
https://doi.org/10.55730/1300-0098.3234
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/13
