Higher Nilpotent Analogues of A-infinity Structure

V. Dolotin; A. Morozov; Sh. Shakirov

doi:10.1016/j.physletb.2007.05.022

paper

Higher Nilpotent Analogues of A-infinity Structure

arXiv:0704.2884 · doi:10.1016/j.physletb.2007.05.022

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 $D_{n} = (I + ε_{n}) d_{n} (I + ε_{n})^{- 1}$ is defined with the help of the $n$ -versions of discrete exterior product $\land_{n}$ and the $K_{n}$ -operator.

preliminary version, essential corrections made

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Analogue of the identity Log Det = Trace Log for resultants