Rings of symmetric functions as modules over the Steenrod algebra
نویسندگان
چکیده
منابع مشابه
Unstable modules over the Steenrod algebra revisited
A new and natural description of the category of unstable modules over the Steenrod algebra as a category of comodules over a bialgebra is given; the theory extends and unifies the work of Carlsson, Kuhn, Lannes, Miller, Schwartz, Zarati and others. Related categories of comodules are studied, which shed light upon the structure of the category of unstable modules at odd primes. In particular, ...
متن کاملDeformation of Symmetric Functions and the Rational Steenrod Algebra
In 1999, Reg Wood conjectured that the quotient of Q[x1, . . . , xn] by the action of the rational Steenrod algebra is a graded regular representation of the symmetric group Sn. As pointed out by Reg Wood, the analog of this statement is a well known result when the rational Steenrod algebra is replaced by the ring of symmetric functions; actually, much more is known about the structure of the ...
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Suppose that A2 is the mod-2 Steenrod algebra, and that R = F2[x1, . . . , xn] is the polynomial ring in n variables over the prime field F2. Campbell and Selick [3] observed that the equations Sqxi = x 2 i−1 for 2≤ i≤ n, and Sqx1 = x 2 n, define an action of A2 on R that makes R isomorphic as an A2-module to the A2-module defined by the standard action on R. In that paper, they also pose the f...
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The algebra S of symmetric invariants over the field with two elements is an unstable algebra over the Steenrod algebra A, and is isomorphic to the mod two cohomology of BO , the classifying space for vector bundles. We provide a minimal presentation for S in the category of unstable A-algebras, i.e., minimal generators and minimal relations. From this we produce minimal presentations for vario...
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Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2008
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2008.8.541