On the structure of $P(n)_\ast P((n))$ for $p=2$
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- by Christian Nassau PDF
- Trans. Amer. Math. Soc. 354 (2002), 1749-1757 Request permission
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.References
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Additional Information
- Christian Nassau
- Affiliation: Johann Wolfgang Goethe-Universität Frankfurt, Fachbereich Mathematik, Robert Mayer Strasse 6-8, 60054 Frankfurt, Germany
- Email: nassau@math.uni-frankfurt.de
- Received by editor(s): July 3, 2000
- Published electronically: January 7, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 1749-1757
- MSC (1991): Primary 55N22; Secondary 55P43
- DOI: https://doi.org/10.1090/S0002-9947-02-02920-3
- MathSciNet review: 1881014