### 抜粋

In a companion paper, we introduced a notion of multi-Dirac structures, a graded version of Dirac structures, and we discussed their relevance for classical field theories. In the current paper we focus on the geometry of multi-Dirac structures. After recalling the basic definitions, we introduce a graded multiplication and a multi-Courant bracket on the space of sections of a multi-Dirac structure, so that the space of sections has the structure of a Gerstenhaber algebra. We then show that the graph of a k-form on a manifold gives rise to a multi-Dirac structure and also that this multi-Dirac structure is integrable if and only if the corresponding form is closed. Finally, we show that the multi-Courant bracket endows a subset of the ring of differential forms with a graded Poisson bracket, and we relate this bracket to some of the multisymplectic brackets found in the literature.

元の言語 | English |
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ページ（範囲） | 1415-1425 |

ページ数 | 11 |

ジャーナル | Journal of Geometry and Physics |

巻 | 61 |

発行部数 | 8 |

DOI | |

出版物ステータス | Published - 2011 8 1 |

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology

## フィンガープリント On the geometry of multi-Dirac structures and Gerstenhaber algebras' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Journal of Geometry and Physics*,

*61*(8), 1415-1425. https://doi.org/10.1016/j.geomphys.2011.03.005