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Non-Degeneracy of 2-Forms and Pfaffian

Department of Mathematics, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Korea
Symmetry 2020, 12(2), 280; https://doi.org/10.3390/sym12020280 (registering DOI)
Received: 8 January 2020 / Revised: 3 February 2020 / Accepted: 10 February 2020 / Published: 13 February 2020
(This article belongs to the Special Issue Advances in Symmetric Tensor Decomposition Methods)
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. View Full-Text
Keywords: Pfaffian; non-degeneracy; symplectic space Pfaffian; non-degeneracy; symplectic space
MDPI and ACS Style

Lee, J.-H. Non-Degeneracy of 2-Forms and Pfaffian. Symmetry 2020, 12, 280.

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