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arXiv · 1001.5264

Matrix De Rham complex and quantum A-infinity algebras

Serguei Barannikov
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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-infinity-algebras, introduced in "Modular operads and Batalin-Vilkovisky geometry" IMRN, Vol. 2007, doi: 10.1093/imrn/rnm075, is represented via de Rham differential acting on the matrix spaces related with Bernstein-Leites simple associative algebras with odd trace q(N), and with gl(N|N). I also show that the Lagrangians of the matrix integrals from "Noncommmutative Batalin-Vilkovisky geometry and Matrix integrals", Comptes Rendus Mathematique, vol 348 (2010), pp. 359-362, arXiv:0912.5484, are equivariantly closed differential forms.

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Serguei Barannikov. 2014-02-02. Matrix De Rham complex and quantum A-infinity algebras. https://doi.org/10.1007/s11005-013-0677-7

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