#
nLab

Poisson Lie 2-algebra

### Context

#### Symplectic geometry

**symplectic geometry**

higher symplectic geometry

## Background

geometry

differential geometry

## Basic concepts

almost symplectic structure, metaplectic structure, metalinear structure

symplectic form, n-plectic form

symplectic Lie n-algebroid

symplectic infinity-groupoid

symplectomorphism, symplectomorphism group

Hamiltonian action, moment map

symplectic reduction, BRST-BV formalism

isotropic submanifold, Lagrangian submanifold, polarization

## Classical mechanics and quantization

Hamiltonian mechanics

quantization

deformation quantization,

**geometric quantization**, higher geometric quantization

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# Contents

## Idea

A $(X, \omega)$ a 2-plectic manifold, its *Poisson Lie 2-algebra* is the higher analog of the Poisson bracket Lie algebra of a symplectic manifold.

For the moment see here for more.

## References

Created on July 2, 2012 at 21:59:36.
See the history of this page for a list of all contributions to it.