Questions tagged [wild-representation-type]
The wild-representation-type tag has no usage guidance.
12
questions
6
votes
1
answer
375
views
Tame-Wild dichotomy; why can't tame algebras be wild?
I would like to understand the Tame-Wild dichotomy, and in particular why an algebra cannot be tame and (semi-)wild at the same time. I've looked in the papers by Drozd and Crawley-Boevey [D80, CB88].
...
6
votes
0
answers
87
views
Condition of indecomposability in the definition of wild representation type
In Tame and wild matrix problems, Drozd defines an algebra $A$ to be wild if there is an $A-k\langle x,y \rangle$-bimodule $M$, such that ${M \otimes}-$ reflects isomorphisms.
Usually I've seen the ...
2
votes
1
answer
213
views
Tame/wild classification of *cyclic* quivers?
There is a famous classification of the path algebras of finite acyclic quivers into finite, tame, and wild representation types. For quivers with cycles, it is standard that the 2-loop quiver (with ...
3
votes
1
answer
153
views
Explicit proof that algebra is derived wild
Following the terminology of
Drozd, Yuriy A., Derived tame and derived wild algebras, Algebra Discrete Math. 2004, No. 1, 57-74 (2004). ZBL1067.16028.
let $A$ and $R$ be algebras over a field $k$. A ...
1
vote
0
answers
358
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
0
answers
97
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
0
answers
50
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
0
answers
37
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
0
answers
40
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
0
answers
107
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
1
answer
827
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
1
answer
689
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-...