On the structure of P(n)*P(n) for p=2

We show that P(n)*(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)*(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) -> P(n). Some consequences for multiplicative and antimultiplicative automorphisms of K(n) for p = 2 are also discussed.

Metadaten
Author:	Christian Nassau
URN:	urn:nbn:de:hebis:30-12069
DOI:	https://doi.org/10.1090/S0002-9947-02-02920-3
ISSN:	1088-6850
ISSN:	0002-9947
Parent Title (English):	Transactions of the American Mathematical Society
Publisher:	Soc.
Place of publication:	Providence, RI
Document Type:	Article
Language:	English
Year of Completion:	2002
Date of first Publication:	2002/01/07
Publishing Institution:	Universitätsbibliothek Johann Christian Senckenberg
Release Date:	2005/07/04
Tag:	Hopf algebroids; Morava K-theory; bordism theory; noncommutative ring spectra
Volume:	354
Issue:	5
Page Number:	9
First Page:	1749
Last Page:	1757
Note:	© 2002 American Mathematical Society
Source:	http://www.ams.org/journals/tran/2002-354-05/home.html
HeBIS-PPN:	358648629
Institutes:	Informatik und Mathematik / Mathematik
Dewey Decimal Classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:	55-XX ALGEBRAIC TOPOLOGY / 55Nxx Homology and cohomology theories [See also 57Txx] / 55N22 Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]
	55-XX ALGEBRAIC TOPOLOGY / 55Pxx Homotopy theory (For simple homotopy type, see 57Q10) / 55P43 Spectra with additional structure (E1, A1, ring spectra, etc.)
Licence (German):	Deutsches Urheberrecht

Open Access