Matrix De Rham Complex and Quantum A-infinity algebras

S. Barannikov

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4 Citations (SciVal)


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 languageEnglish
Pages (from-to)373-395
Number of pages23
JournalLetters in Mathematical Physics
Issue number4
Publication statusPublished - 2014
Externally publishedYes


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


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