Maximal linear subspaces of strong self-dual 2-forms and the Bonan 4-form

BİLGE A. H., Dereli T., Kocak S.

LINEAR ALGEBRA AND ITS APPLICATIONS, vol.434, no.5, pp.1200-1214, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 434 Issue: 5
  • Publication Date: 2011
  • Doi Number: 10.1016/j.laa.2010.11.002
  • Journal Name: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1200-1214
  • Keywords: Bonan form, Self-duality Eight manifolds, 8 DIMENSIONS, EQUATIONS, FIELDS
  • Anadolu University Affiliated: Yes

Abstract

The notion of self-duality of 2-forms in 4-dimensions plays an eminent role in many areas of mathematics and physics, but although the 2-forms have a genuine meaning related to curvature and gauge-field-strength in higher dimensions also, their "self-duality" is something which is almost avoided above 4-dimensions. We show that self-duality of 2-forms is a very natural notion in higher (even) dimensions also and we prove the equivalence of some scattered and rarely used definitions in the literature. We demonstrate the usefulness of this higher self-duality by studying it in 8-dimensions and we derive a natural expression for the Bonan form in terms of self-dual 2-forms and we give an explicit expression of the local action of SO(8) on the Bonan form. (C) 2010 Elsevier Inc. All rights reserved.