NDLI: Matrix De Rham Complex and Quantum A-infinity algebras

Content Provider	Springer Nature Link
Author	Barannikov, S.
Copyright Year	2014
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 $_{∞}$-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\|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.
Ending Page	395
Page Count	23
Starting Page	373
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	4
Volume Number	104
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-01-09
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category homotopy associative algebras Gromov-Witten invariants, quantum cohomology, Frobenius manifolds Theoretical, Mathematical and Computational Physics Statistical Physics, Dynamical Systems and Complexity mirror symmetry. cyclic homology Geometry Batalin–Vilkovisky formalism Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants non-commutative geometry Group Theory and Generalizations matrix integrals Permutations, words, matrices super Lie algebras
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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