A Phenomenon of Reciprocity in the Universal Steenrod Algebra
نویسندگان
چکیده
منابع مشابه
Invariant elements in the dual Steenrod algebra
In this paper, we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${mathcal{A}_p}^*$ under the conjugation map $chi$ and give bounds on the dimensions of $(chi-1)({mathcal{A}_p}^*)_d$, where $({mathcal{A}_p}^*)_d$ is the dimension of ${mathcal{A}_p}^*$ in degree $d$.
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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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While all of the relations in the Steenrod algebra, A, can be deduced in principle from the Adem relations, in practice, it is extremely difficult to determine whether a given polynomial of elements in A is zero for all but the most elementary cases. In his original paper [Mi] Milnor states “It would be interesting to discover a complete set of relations between the given generators of A”. In p...
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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.
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 ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1992
ISSN: 0002-9947
DOI: 10.2307/2153936