Cohomology of the sub-Hopf algebra D of the Steenrod algebra

Let D be the sub-Hopf algebra of the mod 2 Steenrod algebra A generated by image. We are interested in the cohomology of D, image. To obtain information about image, we first filter D by powers of the augmentation ideal and describe the structure of the associated graded Hopf algebra, E0D. E0D is a primitively generated connected Hopf algebra over image and hence corresponds to the restricted Lie algebra of primitive elements, image. We then calculate image and image using a known polynomial algebra complex on the dual of image, image, with differential determined by the bracket in image. We then use the May spectral sequence to obtain results about image and image.