Andrew Salch
We compute the Hochschild homology and cohomology of $A(1)$, the subalgebra of the $2$-primary Steenrod algebra generated by the first two Steenrod squares, $Sq^1$ and $Sq^2$. The computation is accomplished using several May-type spectral sequences.
This paper contains 8 sections, 20 theorems, 48 equations.
Theorem 1
The $\mathbb{F}_2$-vector space dimension of $HH_n(A(1),A(1))$ is: Hence the Poincaré series of the graded $\mathbb{F}_2$-vector space $HH_*(A(1),A(1))$ is If we additionally keep track of the extra grading on $HH_*(A(1),A(1))$ coming from the topological grading on $A(1)$, then the Poincaré series of the bigraded $\mathbb{F}_2$-vector space $HH_{*,*}(A(1),A(1))$ is where $s$ is the homological
