Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On modified extension graphs of a fixed atypicality   In this paper we study extensions between finite-dimensional simple modules
over classical Lie superalgebras $\mathfrak{gl}(m|n), \mathfrak{osp}(M|2n)$ and
$\mathfrak{q}_m$. We consider a simplified version of the extension graph which
is produced from the $Ext^1$-graph by identifying representations obtained by
parity change and removal of the loops. We give a necessary condition for a
pair of vertices to be connected and show that this condition is sufficient in
most of the cases. This condition implies that the image of a
finite-dimensional simple module under the Duflo-Serganova functor has
indecomposable isotypical components. This yields semisimplicity of
Duflo-Serganova functor for $\mathcal{F}in(\mathfrak{gl}(m|n))$ and for
$\mathcal{F}in(\mathfrak{osp}(M|2n))$.

37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex