$$A_\infty $$ A ∞ -Algebra from Supermanifolds

Inspired by the analogy between different types of differential forms on supermanifolds and string fields in superstring theory, we construct new multilinear non-associative products of forms which yield, for a single fermionic dimension, an $$A_\infty $$ -algebra as in string field theory. For multiple fermionic directions, we give the rules for constructing non-associative products, which are the basis for a full $$A_\infty $$ -algebra structure to be yet discussed.