A characterization of simple modules over the Steenrod algebra mod 2
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 کاملA note on the new basis in the mod 2 Steenrod algebra
The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations, denoted by $Sq^n$, between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space. Regarding to its vector space structure over $mathbb{Z}_2$, it has many base systems and some of the base systems can also be restricted to its sub algebras. On the contrary, in ...
متن کاملGlobal structure of the mod two symmetric algebra , H ∗ ( BO ; F 2 ) , over the Steenrod Algebra
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...
متن کاملA Classification of Polynomial Algebras as Modules over the Steenrod Algebra
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...
متن کاملTruncated Polynomial Algebras over the Steenrod Algebra
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology
سال: 1962
ISSN: 0040-9383
DOI: 10.1016/0040-9383(62)90108-8