## Abstract

I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration. In particular, the non-commutative BV-equation, defining the quantum A _{∞}-algebras, introduced in Barannikov (Modular operads and non-commutative Batalin-Vilkovisky geometry. IMRN, vol. 2007, rnm075. Max Planck Institute for Mathematics 2006-48, 2007), is represented via de Rham differential acting on the supermatrix spaces related with Bernstein-Leites simple associative algebras with odd trace q(N), and gl(N{pipe}N). I also show that the matrix Lagrangians from Barannikov (Noncommutative Batalin-Vilkovisky geometry and matrix integrals. Isaac Newton Institute for Mathematical Sciences, Cambridge University, 2006) are represented by equivariantly closed differential forms.

Original language | English |
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Pages (from-to) | 373-395 |

Number of pages | 23 |

Journal | Letters in Mathematical Physics |

Volume | 104 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 |

Externally published | Yes |

## Keywords

- Batalin-Vilkovisky formalism
- cyclic homology
- homotopy associative algebras
- matrix integrals
- mirror symmetry
- non-commutative geometry
- super Lie algebras