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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the realization and classification of symmetric algebras as cohomology rings


Author: Larry Smith
Journal: Proc. Amer. Math. Soc. 87 (1983), 144-148
MSC: Primary 57T15; Secondary 55N99
MathSciNet review: 677250
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Abstract: In this note, we prove that every algebra of the form $ E[\sigma , \ldots ,{\sigma _n}] \otimes P[{\rho _1}, \ldots ,{\rho _n}]$ that is an unstable algebra over the $ \mod p$ Steenrod algebra, $ p$ an odd prime, that satisfies

$\displaystyle \beta {\sigma _i} = {\rho _i},\quad \deg \rho_i \not\equiv 0(p),\quad i = 1, \ldots ,n,$

arises as the cohomology of at least one topological space. Moreover, we show that the classification of such algebras is implicit in the work of Adams and Wilkerson and Clark and Ewing.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0677250-2
PII: S 0002-9939(1983)0677250-2
Article copyright: © Copyright 1983 American Mathematical Society