2 problems

Let $A=\mathbb{C}\oplus\mathfrak{m}$ be a finite-dimensional local algebra of dimension $n$, where $\mathfrak{m}$ is its maximal ideal, and let $\operatorname{Aut}(A)^{\circ}$ deno…

Let $A$ be a local commutative algebra with an $n$-cluster tilting module. Rigidity conjecture. Then $n=1$ and there is an integer $m\geq 1$ such that … The conjecture is one of th…