### Abstract

We describe an extension of the axioms of quantization to the case of 2-plectic manifolds. We show how such quantum spaces can be obtained as stable classical solutions in a zero-dimensional 3-algebra reduced model obtained by dimensional reduction of the Bagger-Lambert-Gustavsson theory. We demonstrate that the groupoid approach to geometric quantization proposed by Hawkins and others can be useful for quantizing 2-plectic manifolds. We discuss our results in the context of recent developments in the quantum geometry of M-branes, and in the nonassociative deformation of spacetime induced by closed strings in the presence of a 2-plectic form.

Original language | English |
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Title of host publication | Progress in Operator Algebras, Noncommutative Geometry, and their Applications |

Editors | Ionel Popescu, Radu Purice |

Publisher | American Mathematical Society |

ISBN (Print) | 978-606-8443-01-0 |

Publication status | Published - 2013 |

Event | 4th Annual Meeting of the European Non Commutative Geometry Network - Bucharest, Romania Duration: 25 Apr 2011 → 30 Apr 2011 |

### Publication series

Name | International Book Series of Mathematical Texts |
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### Conference

Conference | 4th Annual Meeting of the European Non Commutative Geometry Network |
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Country | Romania |

City | Bucharest |

Period | 25/04/11 → 30/04/11 |

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## Cite this

Saemann, C., & J. Szabo, R. (2013). Quantization of 2-plectic manifolds. In I. Popescu, & R. Purice (Eds.),

*Progress in Operator Algebras, Noncommutative Geometry, and their Applications*(International Book Series of Mathematical Texts). American Mathematical Society.