Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On simple-minded systems and $\tau$-periodic modules of self-injective
  algebras   Let $A$ be a finite-dimensional self-injective algebra over an algebraically
closed field, $\mathcal{C}$ a stably quasi-serial component (i.e. its stable
part is a tube) of rank $n$ of the Auslander-Reiten quiver of $A$, and
$\mathcal{S}$ be a simple-minded system of the stable module category
$\stmod{A}$. We show that the intersection $\mathcal{S}\cap\mathcal{C}$ is of
size strictly less than $n$, and consists only of modules with quasi-length
strictly less than $n$. In particular, all modules in the homogeneous tubes of
the Auslander-Reiten quiver of $A$ cannot be in any simple-minded system.

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an