Deformation Bicomplex of Module-algebras

Let H be a bialgebra. An H-module-algebra is an associative algebra A that is also an H-module such that the multiplication map on A becomes an H-module morphism. This algebraic structure arises often in algebraic topology, quantum groups [11, Chapter V.6], Lie and Hopf algebras theory [3, 16, 19], and group representations [1, Chapter 3]. For example, in algebraic topology, the complex cobordism MU(X) of a topological space X is an S -module-algebra, where S is the Landweber-Novikov algebra [13, 17] of stable cobordism operations. Likewise, the singular mod p cohomology H(X; Z/p) of a topological space X is an Ap-module-algebra, where Ap is the Steenrod algebra associated to the prime p [4, 15]. More examples of this form can be found in [2].