Non-Degeneracy of 2-Forms and Pfaffian

Abstract

In this article, we study the non-degeneracy of 2-forms (skew symmetric ( 0 , 2 ) -tensor) α 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.

Keywords

• pfaffian
• non-degeneracy
• symplectic space