$\mathbb{Z}_{2}$-graded identities of the Grassmann algebra over a finite field

Luís Felipe Gonçalves Fonseca

$\mathbb{Z}_{2}$-graded identities of the Grassmann algebra over a finite field

Rings and Algebras 2020-06-19 v3

Authors: Luís Felipe Gonçalves Fonseca

Abstract

Let $F$ be a finite field with characteristic $p > 2$ and let $G$ be the unitary Grassmann algebra generated by an infinite dimensional vector space $V$ over $F$ . In this paper, we determine a basis of the $\mathbb{Z}_{2}$ -graded polynomial identities for any non-trivial $\mathbb{Z}_{2}$ -grading such that a basis of $V$ is homogeneous in this grading.

Keywords

Grassmann algebra Z2-graded identities finite field polynomial identities graded algebra

Cite

@article{arxiv.1403.0888,
  title  = {$\mathbb{Z}_{2}$-graded identities of the Grassmann algebra over a finite field},
  author = {Luís Felipe Gonçalves Fonseca},
  journal= {arXiv preprint arXiv:1403.0888},
  year   = {2020}
}

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