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

摘要

The Leibniz-Hopf algebra is the free associative algebra on one generator, $S^n$, in each positive degree, with coproduct $Delta(S^n) = sum S^j otimes S^{n-j}$. 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 $chi=C circ R$ in this dual Hopf algebra and calculate bases for the fixed points of this algebra under the operations $C$ and $R$.