Young tableaux and homotopy commutative algebras

Abstract

A homotopy commutative algebra, or C∞-algebra, is defined via the Tornike Kadeishvili homotopy transfer theorem on the vector space generated by the set of Young tableaux with self-conjugated Young diagrams {λ: λ = λ'}. We prove that this C∞-algebra is generated in degree 1 by the binary and the ternary operations. © Springer Japan 2013.