Higher nilpotent analogues of [formula omitted]-structure

Abstract

A higher nilpotent analogues of the A ∞ -structure, ( D n ) n = ( ∑ i = 1 ∞ m n ( i ) ) ○ n = 0 , are explicitly defined on arbitrary simplicial complexes, generalizing explicit construction of [V. Dolotin, A. Morozov, Sh. Shakirov, A ∞ structure on simplicial complexes, arXiv:0704.2609, Theor. Math. Phys., in press] for n = 2 . These structures are associated with the higher nilpotent differential m n ( 1 ) = d n , satisfying d n n = 0 , which is naturally defined on triangulated manifolds (tetrahedral lattices), and deformation D n = U n d n U n −1 is defined with the help of the n-versions of exterior product ⋀ n and the K n -operator, U n = I + ⋀ n K n .