The Deformation Complex For DG Hopf Algebras

Details The Deformation Complex For DG Hopf Algebras The Deformation Complex For DG Hopf Algebras

2001-06-29

arxiv.org/abs/math/0106266v2

J. Pure and Applied Algebra, 106 (1966), 199-222

Mathematics

Algebraic Topology

21 pages, 4 figures

Scientific paper

Let H be a differential graded Hopf algebra over a field k. This paper gives an explicit construction of a triple cochain complex that defines the Hochschild-Cartier cohomology of H. A certain truncation of this complex is the appropriate setting for deforming H as an H(q)-structure. The direct limit of all such truncations is the appropriate setting for deforming H as a strongly homotopy associative structure. Sign complications are systematically controlled. The connection between rational perturbation theory and the deformation theory of certain free commutative differential graded algebras is clarified.

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