Some noteworthy alternating trilinear forms

Draisma, Jan; Shaw, Ron

Abstract

Given an alternating trilinear form T ∈ Alt(×3Vn) on Vn =V(n,F) let LT denote the set of T-singular lines in PG(n-1)=PVn, consisting that is of those lines 〈a,b〉 of PG(n-1) such that T(a, b, x) = 0 for all x ∈ Vn. 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.

Citation

Draisma, J., & Shaw, R. (2014). Some noteworthy alternating trilinear forms. Journal of Geometry, 105(1), 167-176. https://doi.org/10.1007/s00022-013-0202-2

• Journal Article Type: Article
• Online Publication Date: Dec 25, 2013
• Publication Date: Apr 1, 2014
• Deposit Date: Jun 29, 2018
• Journal: Journal of Geometry
• Print ISSN: 0047-2468
• Electronic ISSN: 1420-8997
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 1
• Pages: 167-176
• DOI: https://doi.org/10.1007/s00022-013-0202-2
• Keywords: Trivector; Alternating form; Singular line; Division algebra; Desarguesian line-spread
• Public URL: https://hull-repository.worktribe.com/output/901345
• Publisher URL: https://link.springer.com/article/10.1007%2Fs00022-013-0202-2