Algebraic Construction
Smith (2007) gave the following algebraic construction of the Steenrod algebra over a finite field Fq of order q. If V is a vector space over Fq then write SV for the symmetric algebra of V. There is an algebra homomorphism P(x)
such that
for v∈V, where F is the Frobenius endomorphism of SV. If we put
- (for p>2)
or
- (for p=2)
for f∈SV then if V is infinite dimensional the elements Pi generate an algebra isomorphism to the subalgebra of the Steenrod algebra generated by the reduced p′th powers for p odd, or the even Steenrod squares Sq2i for p=2.
Read more about this topic: Steenrod Algebra
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