Higher Nilpotent Analogues of A-infinity Structure

Abstract

Higher nilpotent analogues of the $A-\infty$-structure are explicitly defined on arbitrary simplicial complexes, generalizing explicit construction of /hep-th/0704.2609. These structures are associated with the higher nilpotent differential $d_n$, satisfying $d_n^n=0$, which is naturally defined on triangulated manifolds (tetrahedral lattices). The deformation $D_n=(I+{\epsilon }_n)d_n(I+{\epsilon }_n{)}^{-1}$ is defined with the help of the $n$-versions of discrete exterior product ${\wedge }_n$ and the $K_n$-operator.

preliminary version, essential corrections made

References in corpus (4)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Geometry of Batalin-Vilkovisky quantization
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Cited by in corpus (7)

• Generation of Matrix Models by W-operators
• Unitary Integrals and Related Matrix Models
• Introduction to Integral Discriminants
• Hamiltonian Formalism in the Presence of Higher Derivatives
• Challenges of beta-deformation
• Analogue of the identity Log Det = Trace Log for resultants
• A-infinity structure on simplicial complexes