Some noteworthy alternating trilinear forms
Jan Draisma, Ron Shaw
TL;DR
This paper investigates special classes of alternating trilinear forms on vector spaces, focusing on the geometric properties of their T-singular lines in projective space and identifying noteworthy forms based on their singular line sets.
Contribution
The paper classifies and analyzes particular alternating trilinear forms with unique properties of their T-singular lines in projective geometry.
Findings
Identification of noteworthy classes of alternating trilinear forms
Characterization of T-singular line sets for these forms
Insights into the geometric structure of T-singular lines
Abstract
Given an alternating trilinear form T on the V=F^n let L_T denote the set of T-singular lines in the projective space PV. These are all lines <a,b> for which the linear form T(a,b,.) is identically zero. 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 LT.
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Taxonomy
TopicsFinite Group Theory Research · Algebraic structures and combinatorial models · Advanced Algebra and Geometry