# Contents

## Idea

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

## Definition

###### Definition

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 23:18:20 by Urs Schreiber (89.204.155.76)