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An Alternative Approach To The Adem Relations In The Mod 2 Steenrod Algebra, Neşet Deni̇z Turgay

Turkish Journal of Mathematics

The Leibniz--Hopf algebra F is the free associative algebra over Z on one generator S^n in each degree n>0, with coproduct given by \Delta(S^n) = \sum_{i+j=n} S^i \otimes S^j. We introduce a new perspective on the Adem relations in the mod 2 Steenrod algebra A_2 by studying the map \pi^\ast dual to the Hopf algebra epimorphism \pi: F \otimes Z/2 \to A_2. We also express Milnor's Hopf algebra conjugation formula in A_2^\ast in a different form and give a new approach for the conjugation invariant problem in A_2^\ast.