All Questions

Let $k$ be a field of characteristic zero and $A = kQ$ the path algebra associated with a quiver $Q$. The algebra $A$ is said to be formally smooth over $k$ if $$ \Omega^1_kA = \operatorname{Ker}(\...

Let $A$ be a finite dimensional algebra over an algebraically closed field. I'm trying to better understand the difference between $A$ being representation infinite and $A$ being $\tau$-tilting ...

Let $A$ be a finite dimensional algebra over an algebraically closed field $\mathbb{K}$. Hence, $A$ can be realized as the path algebra of a bound quiver $(Q,I)$, where $I\subseteq\mathbb{K}Q$ is an ...

Let $Q$ be a quiver without oriented cycles. A result of Schofield says that, for dimension vectors $\alpha$ and $\beta$ of $Q$, $\beta\hookrightarrow\alpha$ iff $\operatorname{ext}(\beta, \alpha-\...

Let $A\cong\mathbb{K}Q/I$ be a finite dimensional, associative, basic $\mathbb{K}$ algebra, where $\mathbb{K}$ is algebraically closed and $Q$ is a finite Gabriel quiver on $n$ vertices and $I\...

Let $A$ be a finite dimensional algebra over an algebraically closed field $\mathbb{K}$ of characteristics zero. Suppose $A$ is given by the bound quiver $(Q,I)$. We will use $P_l$ to denote the ...