Polynomial modules over the Steenrod algebra and conjugation in the Milnor basis
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چکیده
منابع مشابه
Polynomial Modules over the Steenrod Algebra and Conjugation in the Milnor Basis
Let Ps = F2 [x1, . . . , xs] be the mod 2 cohomology of the s-fold product of RP∞ with the usual structure as a module over the Steenrod algebra. A monomial in Ps is said to be hit if it is in the image of the action A ⊗ Ps → Ps where A is the augmentation ideal of A. We extend a result of Wood to determine a new family of hit monomials in Ps. We then use similar methods to obtain a generalizat...
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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, ...
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Let $mathcal{A}_p$ be the mod $p$ Steenrod algebra, where $p$ is an odd prime, and let $mathcal{A}$ be the subalgebra $mathcal{A}$ of $mathcal{A}_p$ generated by the Steenrod $p$th powers. We generalize the $X$-basis in $mathcal{A}$ to $mathcal{A}_p$.
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MOHAMED ALI It is shown that the classification of polynomial algebras over the mod p Steenrod algebra is an essentially different problem from the classification of polynomial algebras truncated at height greater than p over the Steenrod algebra . 0 . Introduction . Let B = Zp[y2n y2n2, . . . , y2n,] be a polynomial algebra over A(p), the mod p Steenrod algebra, where yen ; has dimension 2ni a...
متن کاملThe Intersection of the Admissible Basis and the Milnor Basis of the Steenrod Algebra
We prove a conjecture of K. Monks 4] on the relation between the admissible basis and the Milnor basis of the mod 2 Steenrod algebra A 2 , and generalise the result to the mod p Steenrod algebra A p where p is prime. This establishes a necessary and suucient condition for the Milnor basis element P(r 1 ; r 2 ; : : : ; r k) and the admissible basis element P t 1 P t 2 : : : P t k to coincide. Th...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1994
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1994-1207540-3