The homomorphisms between the Dickson-Mùi algebras as modules over the Steenrod algebra.
In: Mathematische Annalen, Jg. 353 (2012-07-01), Heft 3, S. 827-866
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Zugriff:
The Dickson-Mùi algebra consists of all invariants in the mod p cohomology of an elementary abelian p-group under the general linear group. It is a module over the Steenrod algebra, $${\mathcal {A}}$$ . We determine explicitly all the $${\mathcal {A}}$$ -module homomorphisms between the (reduced) Dickson-Mùi algebras and all the $${\mathcal {A}}$$ -module automorphisms of the (reduced) Dickson-Mùi algebras. The algebra of all $${\mathcal {A}}$$ -module endomorphisms of the (reduced) Dickson-Mùi algebra is claimed to be isomorphic to a quotient of the polynomial algebra on one indeterminate. We prove that the reduced Dickson-Mùi algebra is atomic in the meaning that if an $${\mathcal {A}}$$ -module endomorphism of the algebra is non-zero on the least positive degree generator, then it is an automorphism. This particularly shows that the reduced Dickson-Mùi algebra is an indecomposable $${\mathcal {A}}$$ -module. The similar results also hold for the odd characteristic Dickson algebras. In particular, the odd characteristic reduced Dickson algebra is atomic and therefore indecomposable as a module over the Steenrod algebra. [ABSTRACT FROM AUTHOR]
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The homomorphisms between the Dickson-Mùi algebras as modules over the Steenrod algebra.
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Autor/in / Beteiligte Person: | Hu'ng, Nguyễn |
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Zeitschrift: | Mathematische Annalen, Jg. 353 (2012-07-01), Heft 3, S. 827-866 |
Veröffentlichung: | 2012 |
Medientyp: | academicJournal |
ISSN: | 0025-5831 (print) |
DOI: | 10.1007/s00208-011-0698-4 |
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