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

Abstract

The Leibniz-Hopf algebra is the free associative algebra on one generator, S n , in each positive degree, with coproduct .S n / D P S j˝S n j. Let C and R denote coarsening and reversing operations on the mod 2 dual Leibniz-Hopf algebra. We consider decomposition of the Hopf algebra conjugation D C ı R in this dual Hopf algebra and calculate bases for the fixed points of the operations C and R.

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

“…The above equality is already given in [42,Section 2]. We give a combinatoric proof for this identity.…”

“…Results concerning conjugation in the mod 2 dual Leibniz-Hopf algebra. Recall from [42,Section 2] that, conjugation operation in F * 2 has a decomposition χ F * 2 = C • R, where C is a coarsening operation. Given a basis element S b1,...,bp , its image under the coarsening operation C is given by…”