Steenrod Algebra - Algebraic Construction

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 vV, where F is the Frobenius endomorphism of SV. If we put

(for p>2)

or

(for p=2)

for fSV 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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