Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived factorization categories of non-Thom--Sebastiani-type sums of
  potentials   We first prove semi-orthogonal decompositions of derived factorization
categories arising from sums of potentials of gauged Landau-Ginzburg models,
where the sums are not necessarily Thom--Sebastiani type. We then apply the
result to the category $\HMF^{L_f}(f)$ of maximally graded matrix
factorizations of an invertible polynomial $f$ of chain type, and explicitly
construct a full strong exceptional collection $E_1,\hdots,E_{\mu}$ in
$\HMF^{L_f}(f)$ whose length $\mu$ is the Milnor number of the
Berglund--H\"ubsch transpose $\widetilde{f}$ of $f$. This proves a conjecture,
which postulates that for an invertible polynomial $f$ the category
$\HMF^{L_f}(f)$ admits a tilting object, in the case when $f$ is a chain
polynomial. Moreover, by careful analysis of morphisms between the exceptional
objects $E_i$, we explicitly determine the quiver with relations $(Q,I)$ which
represents the endomorphism ring of the associated tilting object
$\oplus_{i=1}^{\mu}E_i$ in $\HMF^{L_f}(f)$, and in particular we obtain an
equivalence $\HMF^{L_f}(f)\cong \Db(\fmod kQ/I)$.

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The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
11
The categories of this paper are: hep-lat