Reference : Multi-oriented props and homotopy algebras with branes |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/33801 | |||

Multi-oriented props and homotopy algebras with branes | |

English | |

Merkulov, Sergei [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Mar-2020 | |

Letters in Mathematical Physics | |

Kluwer Academic Publishers | |

110 | |

1425-1475 | |

Yes (verified by ORBi^{lu}) | |

International | |

0377-9017 | |

1573-0530 | |

Dordrecht | |

Netherlands | |

[en] algebra, operad, homotopy theory | |

[en] We introduce a new category of differential graded {\em multi-oriented}\, props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a collection of $k$ linear subspaces
in that space, $k$ being the number of extra directions (if $k=0$ this structure recovers an ordinary prop); symplectic vector spaces equipped with $k$ Lagrangian subspaces play a distinguished role in this theory. Manin triples is a classical example of an algebraic structure (concretely, a Lie bialgebra structure) given in terms of a vector space and its subspace; in the context of this paper Manin triples are precisely symplectic Lagrangian representations of the {\em 2-oriented} generalization of the classical operad of Lie algebras. In a sense, the theory of multi-oriented props provides us with a far reaching strong homotopy generalization of Manin triples type constructions. | |

Researchers | |

http://hdl.handle.net/10993/33801 |

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