n-plectic vector space

The generalization of the notion of symplectic vector space from symplectic geometry to n-plectic geometry.

For $n \in \mathbb{N}$, an **n-plectic vector space** is a vector space $V$ (over the real numbers) equipped with an $(n+1)$-linear skew function

$\omega : \wedge^{n+1} V \to \mathbb{R}$

such that regarded as a function

$V \to \wedge^n V^*$

is has trivial kernel.

Created on March 2, 2012 at 23:18:20. See the history of this page for a list of all contributions to it.