## Abstract

We develop a new formalism for the quantum master equation Δ e
^{S}
^{/}
^{ħ}
= 0 and the category of IBL
_{∞}
-algebras and simplify some homotopical algebra arising in the context of oriented surfaces with boundary. We introduce and study a category of MV-algebras, which, on the one hand, contains such important categories as those of IBL
_{∞}
-algebras and L
_{∞}
-algebras and, on the other hand, is homotopically trivial, in particular allowing for a simple solution of the quantum master equation. We also present geometric interpretation of our results.

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

Pages (from-to) | 1515-1543 |

Number of pages | 29 |

Journal | Letters in Mathematical Physics |

Volume | 107 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2017 |

## Keywords

- IBL -algebra
- MV -algebra
- Master equation
- Transfer