Matrix De Rham complex and quantum A-infinity algebras
Quantum Algebra
2014-02-04 v2 Representation Theory
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.
Cite
@article{arxiv.1001.5264,
title = {Matrix De Rham complex and quantum A-infinity algebras},
author = {Serguei Barannikov},
journal= {arXiv preprint arXiv:1001.5264},
year = {2014}
}
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