On the structure of for

Author:
Christian Nassau

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

Published electronically:
January 7, 2002

MathSciNet review:
1881014

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Abstract: We show that for with its geometrically induced structure maps is *not* an Hopf algebroid because neither the augmentation nor the coproduct are multiplicative. As a consequence the algebra structure of is slightly different from what was supposed to be the case. We give formulas for and and show that the inversion of the formal group of is induced by an antimultiplicative involution . Some consequences for multiplicative and antimultiplicative automorphisms of for are also discussed.

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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

DOI:
https://doi.org/10.1090/S0002-9947-02-02920-3

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

Received by editor(s):
July 3, 2000

Published electronically:
January 7, 2002

Article copyright:
© Copyright 2002
American Mathematical Society