Applications of Hochschild cohomology to the moduli of subalgebras of the full matrix ring

Kazunori Nakamoto, Takeshi Torii

Let ${\mathrm{Mold}}_{n,d}$ be the moduli of rank $d$ subalgebras of ${\mathrm{M}}_n$ over $\mathbb{Z}$. For $x\in {\mathrm{Mold}}_{n,d}$, let $\mathcal{A}(x)\subseteq {\mathrm{M}}_n(k(x))$ be the…