Nonsingular bilinear maps revisited

Carlos Domínguez, Kee Yuen Lam

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A bilinear map Φ : ℝr × ℝs → ℝn is nonsingular if Φ(a , b) = 0 implies a = 0 or b = 0. These maps are of interest to topologists, and are instrumental for the study of vector bundles over real projective spaces. The main purpose of this paper is to produce examples of such maps in the range 24 ≤ r ≤ 32, 24 ≤ s ≤ 32 using the arithmetic of octonions (otherwise known as Cayley numbers) as an effective tool. While previous constructions in lower dimensional cases use ad hoc techniques, our construction follows a systematic procedure and subsumes those techniques into a uniform perspective.

Original languageEnglish
Pages (from-to)377-390
Number of pages14
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume151
Issue number1
DOIs
StatePublished - Feb 2021

Keywords

  • Bilinear maps
  • Immersion
  • Polynomial product
  • Projective spaces
  • Vector bundles

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