Matrix De Rham complex and quantum A-infinity algebras

Details Matrix De Rham complex and quantum A-infinity algebras Matrix De Rham complex and quantum A-infinity algebras

2010-01-28

arxiv.org/abs/1001.5264v1

Mathematics

Quantum Algebra

preprint HAL-00378776, (04/2009), submitted for publication on 20/01/10

Scientific paper

I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration and, in particular, represent the non-commutative BV-equation, introduced in my previous papers and defining the quantum A-infinity-algebras, via de Rham differential acting on the supermatrix spaces related with Bernstein-Leites simple associative algebras with odd trace, and gl(N|N). I give a noncommutative super-equivariant AKSZ-type symplectic sigma-model interpretation of the lagrangians of supersymmetric matrix models from my previous paper.

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