A Remark on the Conjugation in the Steenrod Algebra

Abstract

Abstract. We investigate the Hopf algebra conjugation, χ, of the mod 2 Steenrod algebra, A 2 , in terms of the Hopf algebra conjugation, χ ′ , of the mod 2 Leibniz-Hopf algebra. We also investigate the fixed points of A 2 under χ and their relationship to the invariants under χ ′ .

Invariants under decomposition of the conjugation in the mod 2 dual Leibniz-Hopf Algebra

“…In [16,Section 6] the author and Kaji introduced an explicit correspondence between the invariant elements of F 2 and of F 2 under the Hopf algebra conjugation operation. See also [15] for the relationship between the conjugation invariants in F 2 and the conjugation invariants in the mod 2 Steenrod algebra.…”

On the mod p Steenrod algebra and the Leibniz-Hopf algebra

“…Let us (briefly) give information about it. When p = 2, in an earlier paper [39,Section 3], the homomorphism π is considered for determining a better formula for the conjugation operation in the Steenrod algebra. In the same paper, the conjugation invariant problem in A 2 is also investigated by using the conjugation invariants in the Leibniz-Hopf algebra [10].…”