A note on the new basis in the mod 2 Steenrod algebra
محورهای موضوعی : Algebraic topology
T. Vergili
1
(Department of Mathematics, Faculty of Science, Ege University, Turkey)
I. Karaca
2
(Department of Mathematics, Faculty of Science, Ege University, Turkey)
کلید واژه: Steenrod algebra, cohomology operations, Hopf algebra,
چکیده مقاله :
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 addition to the work of Wood, in this paper we define a new base system for the Hopf subalgebras $\mathcal{A}(n)$ of the mod $2$ Steenrod algebra which can be extended to the entire algebra. The new base system is obtained by defining a new linear ordering on the pairs $(s+t,s)$ of exponents of the atomic squares $Sq^{2^s(2^t-1)}$ for the integers $s\geq 0$ and $t\geq 1$.
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