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 Delta(S-n) = Sigma S-j circle times Sn-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 o R in this dual Hopf algebra and calculate bases for the fixed points of the operations C and R.