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I'm reading a paper of Aidan Schofield "General Representations of Quivers" and he defines quiver representation over any commutative ring. See the below image. Towards the end, he has this representa …

I was wondering what are some of the hot topics in quiver representation or representation theory of algebras that can lead to good mathematics and is important to many mathematicians and top mathemat …

Consider the affine space given by four $2\times 2$ matrices, i.e., $\mathbb{A}^{16}\cong M(\mathbb{C})_{2\times 2}^4$. Now, consider the algebraic set $V$ given by the vanishing of the relation $AB- …

I'm trying to compute some examples and I'm unable to come up with a following example: What is(are) the example(s) of an acyclic quiver $Q$ with relations such that the 2-Kronecker quiver is NOT a su …

I wanted to know some references where people have studied the representation theory of tame concealed algebra of Euclidean type. What do we know about the structure of their module category? What ki …

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 infini …

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-\bet …

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 indec …

I'm reading a paper of Aidan Schofield- "General Representations of Quivers" and I'm trying to understand the proof of Theorem 3.3. I'm having trouble understanding the argument that's underlined in t …

I have a vague question: Let $X$ be an algebraic pre-scheme and $G$ be a linear reductive group. Consider the G.I.T. quotient $X{/\!/}G$. Is there any result (maybe in some special case) which tells u …

I have been studying hyperplane arrangements from R. Stanley's notes and so far, I have read until lecture 5. But, Lecture 6 and end of Lecture 5 seems very combinatorial. I'm more interested in the " …

I'm asking this question as a continuation of discussion and answer given by Hugh Thomas at the following post: Why do people study semi-invariant ring (in general)? I have been studying about semi-in …

Let $A=\mathbb{K}Q$ be the path algebra of an acyclic quiver $Q$ over an algebraically closed field $\mathbb{K}$, and $0\not=I\subset\mathbb{K}Q$ be an admissible ideal. Let $W$ be a left $A$-module a …

Let $G$ be a linearly reductive algebraic group, and let $X$ be an irreducible affine variety, over an algebraically closed field $\mathbb{K}$, with a regular action of $G$. By Rosenlicht's result, we …