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On the structure of
Authors:Christian Nassau
Affiliation:Johann Wolfgang Goethe-Universität Frankfurt, Fachbereich Mathematik, Robert Mayer Strasse 6-8, 60054 Frankfurt, Germany
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.

Keywords:Hopf algebroids   Morava $K$-theory   bordism theory   noncommutative ring spectra
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