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

Luís Felipe Gonçalves Fonseca

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

Rings and Algebras 2017-07-25 v1

Authors: Luís Felipe Gonçalves Fonseca

Abstract

Let $F$ be a finite field with the 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 for $\mathbb{Z}_{2}$ -graded polynomial identities for any non-trivial $\mathbb{Z}_{2}$ -grading such that its underlying vector space is homogeneous.

Keywords

$\mathbb{Z}_{2}$-graded identities Grassmann algebra finite field polynomial identities homogeneous vector space

Cite

@article{arxiv.1707.07652,
  title  = {$\mathbb{Z}_{2}$-graded identities of the Grassmann algebra over a finite field (update version)},
  author = {Luís Felipe Gonçalves Fonseca},
  journal= {arXiv preprint arXiv:1707.07652},
  year   = {2017}
}

Comments

15 pages. arXiv admin note: text overlap with arXiv:1403.0888

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