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Journal of Geometry

, Volume 105, Issue 1, pp 167–176 | Cite as

Some noteworthy alternating trilinear forms

  • Jan DraismaEmail author
  • Ron Shaw
Article

Abstract

Given an alternating trilinear form \({T\in\text{Alt}(\times^{3}V_{n})}\) on \({V_{n}=V(n,\mathbb{F})}\) let \({\mathcal{L}_{T}}\) denote the set of T-singular lines in \({\text{PG}(n-1)=\mathbb{P}V_{n},}\) consisting that is of those lines \({\langle a,b\rangle}\) of \({\text{PG}(n-1)}\) such that T(a, b, x) = 0 for all \({x\in V_{n}.}\) Amongst the immense profusion of different kinds of T we single out a few which we deem noteworthy by virtue of the special nature of their set \({\mathcal{L}_{T}}\).

Mathematics Subject Classification (2010)

15A69 17A35 51E23 

Keywords

Trivector alternating form singular line division algebra Desarguesian line-spread 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenTheNetherlands
  2. 2.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  3. 3.Centre for MathematicsUniversity of HullHullUK

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