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Maximal Linear Subspaces of Strong Self-Dual 2-forms and the Bonan 4-form

✍ Scribed by Ayşe Hümeyra Bilge; Tekin Dereli; Şahin Koçak

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
253 KB
Volume
434
Category
Article
ISSN
0024-3795

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✦ Synopsis

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 gaugefield-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 selfdual 2-forms and we give an explicit expression of the local action of SO(8) on the Bonan form.

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