# Variations of the bridge quiver for domestic string algebras

@inproceedings{Sardar2021VariationsOT, title={Variations of the bridge quiver for domestic string algebras}, author={Shantanu Sardar and Amit Kuber}, year={2021} }

In the computation of some representation-theoretic numerical invariants of domestic string algebras, a finite combinatorial gadget introduced by Schröer– the bridge quiver whose vertices are (representatives of cyclic permutations of) bands and whose arrows are certain band-free strings–has been used extensively. There is a natural but ill-behaved partial binary operation, ○, on the larger set of weak bridges such that bridges are precisely the ○-irreducibles. With the goal of computing… Expand

#### References

SHOWING 1-10 OF 11 REFERENCES

String algebras in representation theory

- Mathematics
- 2016

The work in this thesis is concerned with three subclasses of the string algebras: domestic string algebras, gentle algebras and derived-discrete algebras (of non-Dynkin type). The various questions… Expand

Maps between tree and band modules

- Mathematics
- 1991

The indecomposable modules over special biserial algebras are known to be of a specially simple form, so-called “tree” and “band” modules (cf. [6,2]). Crawley-Boevey has shown how to describe the… Expand

Krull-Gabriel dimension of domestic string algebras

- Mathematics
- 2015

We calculate, confirming a conjecture of Schr\"{o}er, the Krull-Gabriel dimension of the category of modules over any domestic string algebra, as well as the Cantor-Bendixson rank of each point of… Expand

On the Infinite Radical of a Module Category

- Mathematics
- 2000

Let $k$ be an algebraically closed field, and let
$A$ be a finite-dimensional $k$-algebra.
The first aim of classsical representation theory was to classify all indecomposable $A$-modules, but the… Expand

INDECOMPOSABLE REPRESENTATIONS OF THE LORENTZ GROUP

- Mathematics
- 1968

Let be the Lie algebra of the Lorentz group or, what is the same, of the group . We denote by the Lie algebra of its maximal compact subgroup, that is, of . Let be the finite-dimensional irreducible… Expand

Serial functors, Jacobson radical and representation type

- Mathematics
- 2002

It is an important problem in representation theory to relate the representation type of a k-algebra A to dimensions of finitely presented functors from mod(A) to mod(k). We prove that a string… Expand

Band combinatorics of domestic string algebras

- Mathematics
- 2007

We prove that the multiplicity of a simple module as a composition factor in a composition series for a primitive band module over a domestic string algebra is at most two.

On the Stable Radical of Some Non-Domestic String Algebras

- Mathematics
- 2020

We introduce the concept of a prime band in a string algebra $\Lambda$ and use it to associate to $\Lambda$ its finite bridge quiver. Then we introduce a new technique of `recursive systems' for… Expand

On the factorization of graph maps for domestic string algebras

- Colloq . Math .
- 2007