# Contents

## Idea

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

## Definition

###### Definition

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

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

such that regarded as a function

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

is has trivial kernel.

Created on March 2, 2012 23:18:20 by Urs Schreiber (89.204.155.76)