The Koszul–Tate type resolution for Gerstenhaber–Batalin–Vilkovisky algebras

Enhanced homotopy theory for period integrals of smooth projective hypersurfaces

“…In fact, (Ω • [y ,x ]/ , D S ) is the Chevalley-Eilenberg complex associated to the Lie algebra representation ρ X which computes the Lie algebra cohomology and, on the other hand, ( X , K X ) is the dual Chevalley-Eilenberg complex which computes the Lie algebra homology 20. If n = 1, then the same result holds except dim H −1 KX ( X ) = dim H 0 KX ( X ) + 1; see (1.12),[1].…”

“…Jeehoon Park and Donggeon Yhee proved that one has to add infinitely many new formal variables to make a BV resolution of ( X , ·, K X ). See[20] for a precise meaning of such a BV resolution.…”

“…Assume that n > 1. 20 Then we have the following description of the total cohomology of ( X , K X ):…”