Brace Operations and Deligne’s Conjecture for Module-algebras

Let H be a bialgebra and let A be an associative algebra. The algebra A is said to be an H-module-algebra if there is an H-module structure on A such that the multiplication on A becomes an H-module morphism. For example, if S denotes the Landweber-Novikov algebra [15, 21], then the complex cobordism MU(X) of a topological space X is an S module-algebra. Likewise, the singular mod p cohomology H(X; Fp) of a topological space X is an Ap-module-algebra, where Ap denotes the Steenrod algebra associated to the prime p [7, 19]. Other similar examples from algebraic topology can be found in [4]. Important examples of module-algebras from Lie and Hopf algebras theory can be found in, e.g., [12, V.6].