Matrix De Rham complex and quantum A-infinity algebras

Serguei Barannikov (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We represent the noncommutative Batalin-Vilkovisky equation, defining the quantum A-infinity algebras with odd inner product from our previous work, via GL-invariant tensors on matrix spaces gl(n|n)(A). We identify the Batalin-Vilkovisky differential with the GL-invariant DeRham differential on the matrix spaces. In the even case the super Lie algebra gl(n|n)(A) with the functional given by trace is replaced by the "strange odd" super Lie algebra q(n) with odd trace. As a consequence I give a noncommutative super-equivariant AKSZ-type symplectic sigma-model interpretation of the lagrangians of supersymmetric matrix models from my previous paper.

Domaines: Géométrie algébrique [math.AG]; Algèbres quantiques [math.QA]

Serguei Barannikov. Matrix De Rham complex and quantum A-infinity algebras. 2008. ⟨hal-00378776⟩