On the structure of \(P(n)_\ast P(n)\) for \(p = 2\)
Abstract
We show that \(P(n)_\ast (P(n))\) for \(p=2\) with its geometrically induced structure maps is not an Hopf algebroid because neither the augmentation \(\epsilon\) nor the coproduct \(\Delta\) are multiplicative. As a consequence the algebra structure of \(P(n)_\ast (P(n))\) is slightly different from what was supposed to be the case. We give formulas for \(\epsilon (xy)\) and \(\Delta (xy)\) and show that the inversion of the formal group of \(P(n)\) is induced by an antimultiplicative involution \(\Xi :P(n)\rightarrow P(n)\). Some consequences for multiplicative and antimultiplicative automorphisms of \(K(n)\) for \(p=2\) are also discussed.