### Abstract

Using the technique of higher derived brackets, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic 2-manifold. The algebra we obtain accommodates the Dorfman bracket of a Courant algebroid as the binary operation in the hierarchy of operations, and the defect in the symmetry of each operation is measurable in a certain precise sense. We move to call such an algebra a homotopy Dorfman algebra, or a D1-algebra, which leads to the construction of a homotopy Courant algebroid.

Original language | English (US) |
---|---|

Pages (from-to) | 133-156 |

Number of pages | 24 |

Journal | Rendiconti di Matematica e delle Sue Applicazioni |

Volume | 39 |

Issue number | 1 |

State | Published - Jan 1 2018 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory
- Modeling and Simulation
- Geometry and Topology
- Fluid Flow and Transfer Processes
- Discrete Mathematics and Combinatorics
- Computational Mathematics
- Applied Mathematics

### Cite this

*Rendiconti di Matematica e delle Sue Applicazioni*,

*39*(1), 133-156.

}

*Rendiconti di Matematica e delle Sue Applicazioni*, vol. 39, no. 1, pp. 133-156.

**Homotopy Loday algebras and higher Dorfman brackets.** / Peddie, Matthew.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Homotopy Loday algebras and higher Dorfman brackets

AU - Peddie, Matthew

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Using the technique of higher derived brackets, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic 2-manifold. The algebra we obtain accommodates the Dorfman bracket of a Courant algebroid as the binary operation in the hierarchy of operations, and the defect in the symmetry of each operation is measurable in a certain precise sense. We move to call such an algebra a homotopy Dorfman algebra, or a D1-algebra, which leads to the construction of a homotopy Courant algebroid.

AB - Using the technique of higher derived brackets, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic 2-manifold. The algebra we obtain accommodates the Dorfman bracket of a Courant algebroid as the binary operation in the hierarchy of operations, and the defect in the symmetry of each operation is measurable in a certain precise sense. We move to call such an algebra a homotopy Dorfman algebra, or a D1-algebra, which leads to the construction of a homotopy Courant algebroid.

UR - http://www.scopus.com/inward/record.url?scp=85057721203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057721203&partnerID=8YFLogxK

M3 - Article

VL - 39

SP - 133

EP - 156

JO - Rendiconti di Matematica e delle Sue Applicazioni

JF - Rendiconti di Matematica e delle Sue Applicazioni

SN - 1120-7183

IS - 1

ER -