Some quotient Hopf algebras of the dual Steenrod algebra

Some Quotient Hopf Algebras of the Dual Steenrod Algebra

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...

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 $d$‎.

On the Coderivations of Some Hopf Algebras

Sub-Hopf algebras of the Steenrod algebra and the Singer transfer

Let A denote the mod 2 Steenrod algebra (see Steenrod and Epstein [28]). The problem of computing its cohomology H∗,∗(A) is of great importance in algebraic topology, for this bigraded commutative algebra is the E2 term of the Adams spectral sequence (see Adams [1]) converging to the stable homotopy groups of spheres. But despite intensive investigation for nearly half a century, the structure ...

Truncated 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...