An alternative approach to the Adem relations in the mod 2 Steenrod algebra

Authors : Neşet Deniz TURGAY

Pages : 924-934

Doi:10.3906/mat-1309-6

View : 10 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :The Leibniz--Hopf algebra F is the free associative algebra over Z on one generator Sn in each degree n>0, with coproduct given by Dinsert ignore into journalissuearticles values(Sn); = \sumi+j=n Si \otimes Sj. We introduce a new perspective on the Adem relations in the mod 2 Steenrod algebra A2 by studying the map p\ast dual to the Hopf algebra epimorphism p: F \otimes Z/2 \to A2. We also express Milnor`s Hopf algebra conjugation formula in A2\ast in a different form and give a new approach for the conjugation invariant problem in A2\ast.
Keywords : Adem relations, Hopf algebra, Leibniz Hopf algebra, antipode, Steenrod algebra, quasisymmetric functions