The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra
نویسندگان
چکیده
منابع مشابه
A 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 ...
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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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Fix a prime p, and let A be the polynomial part of the dual Steenrod algebra. The Frobenius map on A induces the Steenrod operation P̃0 on cohomology, and in this paper, we investigate this operation. We point out that if p = 2, then for any element in the cohomology of A, if one applies P̃0 enough times, the resulting element is nilpotent. We conjecture that the same is true at odd primes, and t...
متن کاملThe Cohomology Algebra of a Subalgebra of the Steenrod Algebra
We compute the cohomology algebra of P (1), the subalgebra of the Steenrod algebra generated by P 1 and P p. This completes a partial result given by Arunas Liulevicius in 1962 and provides explicit representatives in the cobar construction for all but one of the algebra generators.
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ژورنال
عنوان ژورنال: Journal of Homotopy and Related Structures
سال: 2016
ISSN: 2193-8407,1512-2891
DOI: 10.1007/s40062-016-0163-x