nLab
n-plectic vector space

Contents

Idea

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

Definition

Definition

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

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

such that regarded as a function

V nV * V \to \wedge^n V^*

is has trivial kernel.

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