Homotopy Loday algebras and higher Dorfman brackets

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)133-156
Number of pages24
JournalRendiconti di Matematica e delle Sue Applicazioni
Volume39
Issue number1
StatePublished - Jan 1 2018

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Brackets
Algebra
Homotopy
Binary operation
Defects
Symmetry

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

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

In: Rendiconti di Matematica e delle Sue Applicazioni, Vol. 39, No. 1, 01.01.2018, p. 133-156.

Research output: Contribution to journalArticle

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