Annihilators of Principal Ideals in the Exterior Algebra

Abstract

Abstract. In this paper we describe annihilators of principal ideals of exterior algebras. For odd elements we establish formulae for dimensions of their principal ideals and their annihilators. For even elements we exhibit (multiplicative) generators for annihilator ideals.

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

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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].

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“…Further if B is also symmetric the algebra is called a symmetric algebra. The exterior algebra is an important example of Frobenius algebras [3]. First of all we note that A is a symmetric algebra.…”

“…In [3], we proved that when F is a field of characteristic zero the annihilator of even neat element µ, i.e, n 1 , n 2 , . .…”

“…(iii) to describe the vector space structure of both the principal ideal (µ) and its annihilator Ann(µ) in E(V ) by using stack-sortable polynomials introduced in [3] and the results of [2].…”

Generalized Catalan Numbers

“…. ς kt when Char(F ) = 0 (see [1]). Dimensions of subspaces of E(V ) spanned by certain elements of this type can be used to extend results of [1] to remove the restriction Char(F ) = 0.…”