Minimal Generators of Annihilators of Neat Even Elements in The Exterior Algebra

TL;DR

This paper identifies a minimal generating set for the annihilators of even neat elements in the exterior algebra over a field of positive characteristic, confirming a previous conjecture and providing a basis for these annihilators.

Contribution

It presents the first explicit minimal generators for these annihilators in positive characteristic, confirming a prior conjecture and building on earlier results.

Findings

Established a minimal generating set for the annihilators.

Provided a basis for the annihilators.

Confirmed the conjecture from previous work.

Abstract

In this paper we exhibit a minimal set of generators form the annihilator of even neat elements of the exterior algebra of a vector space, when the base field is of positive characteristic and thus we prove the conjecture we established in [3]. In order to do that we heavily use the results obtained in [1] and [2]. This also allows us to exhibit a vector space basis for the annihilators under consideration.