Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [wild-representation-type]

The tag has no usage guidance.

1
vote
0answers
106 views

Infinite-dimensional representation theory of $K[x]$

Let $K$ be an algebraically closed field. The finite-dimensional representation theory of the polynomial algebra $K[x]$ is tame and completely understood, which I shall first summarise. It's ...
3
votes
0answers
82 views

Infinite-dimensional wild commutative algebras with non-trivial units

Let $A$ be an arbitrary (not necessarily finite-dimensional) associative algebra over an algebraically closed field $K$, and let $\mathrm{fin\,}A$ denote the category of finite-dimensional $A$-modules....
1
vote
0answers
40 views

Regular partial tilting modules in wild hereditary algebras

Let $k$ be an algebraically closed field. Let $Q$ be a connected wild quiver. Let $\mathcal{R}_1$, $\mathcal{R}_2$ be two regular components of the Auslander-Reiten quiver of $kQ$ that contain stones. ...
2
votes
0answers
35 views

Morphisms from quasi-simple regular rigid $\Lambda$-module $M$ to $\tau^m M$ when $\Lambda$ is wild hereditary

Let $\Lambda$ be a finite dimensional basic wild hereditary algebra and $M$ be an indecomposable regular quasi-simple right-$\Lambda$ that is rigid in a regular component $\mathcal{R_i}$ of the ...
2
votes
0answers
34 views

Predecessors and Successors of regular silting objects in bounded derived categories of wild hereditary algebras

Let $\Lambda$ be a wild hereditary algebra and let $T$ be one of its regular silting objects (i.e. all indecomposable direct summands of $T$ are shifts of indecomposable regular modules). What do we ...
3
votes
0answers
83 views

Tensor Functors and Representations of Wild Quivers

A finite-dimensional $K$-algebra $A$ is of wild representation type if and only if there exists a $K\left<t_1,t_2\right>$-$A$-bimodule $_{K\left<t_1,t_2\right>}M_A$ such that the left $K\...
3
votes
1answer
448 views

Is it possible to classify the indecomposable representations of the wild quiver with one vertex and two arrows using infinite sets of parameters?

I have read several other questions about wild representation type but may I ask..what actually can be done and what have been done (such as partial results) about classifying indecomposable ...
13
votes
1answer
414 views

Why is the A6 preprojective algebra of wild representation type?

As mentioned in the title, I would like to know a proof of the "well known" fact that the A6 preprojective algebra is of wild representation type. Ideally, I would like to see an explicit two-...