- Turkish Journal of Mathematics
- Vol: 38 Issue: 5
- An alternative approach to the Adem relations in the mod 2 Steenrod algebra
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 : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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 D(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