Steenrod Algebra - Adem Relations

Adem Relations

The Adem relations for p=2 were conjectured by Wu (1952) and proved by José Adem (1952) and are given by

for all i, j > 0 such that i < 2j. (The binomial coefficients are to be interpreted mod 2.) The Adem relations allow one to write an arbitrary composition of Steenrod squares as a sum of Serre-Cartan basis elements.

For odd p the Adem relations are

for a<pb and

for a≤pb