Non-degeneracy of 2-forms and pfaffian

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Abstract

In this article, we study the non-degeneracy of 2-forms (skew symmetric (0, 2)-tensor) a along the Pfaffian of α. We consider a symplectic vector space V with a non-degenerate skew symmetric (0, 2)-tensor ω, and derive various properties of the Pfaffian of α. As an application we show the non-degenerate skew symmetric (0, 2)-tensor ω has a property of rigidity that it is determined by its exterior power.

Original languageEnglish
Article number280
JournalSymmetry
Volume12
Issue number2
DOIs
StatePublished - 1 Feb 2020

Bibliographical note

Publisher Copyright:
© 2020 by the authors.

Keywords

  • Non-degeneracy
  • Pfaffian
  • Symplectic space

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