Automorphisms and superalgebra structures on the Grassmann algebra

Guimarães, Alan; Koshlukov, Plamen

doi:10.48550/arxiv.2009.00175

Search citation statements

Order By: Relevance

Paper Sections

Select...

Preliminaries1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall that the Grassmann algebra has other gradings by the group Z 2 . Here we are not going to discuss these constructions (since we will not need them here) but instead, we refer the reader to [14,22].…”

Section: Preliminariesmentioning

confidence: 99%

Graded identities for algebras with elementary gradings over an infinite field

Diniz¹,

Fidelis

Koshlukov³

2022

Proceedings of the Edinburgh Mathematical Society

Self Cite

View full text Add to dashboard Cite

Let $F$ be an infinite field of positive characteristic $p > 2$ and let $G$ be a group. In this paper, we study the graded identities satisfied by an associative algebra equipped with an elementary $G$ -grading. Let $E$ be the infinite-dimensional Grassmann algebra. For every $a$ , $b\in \mathbb {N}$ , we provide a basis for the graded polynomial identities, up to graded monomial identities, for the verbally prime algebras $M_{a,b}(E)$ , as well as their tensor products, with their elementary gradings. Moreover, we give an alternative proof of the fact that the tensor product $M_{a,b}(E)\otimes M_{r,s}(E)$ and $M_{ar+bs,as+br}(E)$ are $F$ -algebras which are not PI equivalent. Actually, we prove that the $T_{G}$ -ideal of the former algebra is contained in the $T$ -ideal of the latter. Furthermore, the inclusion is proper. Recall that it is well known that these algebras satisfy the same multilinear identities and hence in characteristic 0 they are PI equivalent.

show abstract

Section: Preliminariesmentioning

confidence: 99%