Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized McKay Quivers, Root System and Kac-Moody Algebras   Let $Q$ be a finite quiver and $G\subseteq\Aut(\mathbbm{k}Q)$ a finite
abelian group. Assume that $\hat{Q}$ and $\Gamma$ is the generalized Mckay
quiver and the valued graph corresponding to $(Q, G)$ respectively. In this
paper we discuss the relationship between indecomposable
$\hat{Q}$-representations and the root system of Kac-Moody algebra
$\mathfrak{g}(\Gamma)$. Moreover, we may lift $G$ to
$\bar{G}\subseteq\Aut(\mathfrak{g}(\hat{Q}))$ such that $\mathfrak{g}(\Gamma)$
embeds into the fixed point algebra $\mathfrak{g}(\hat{Q})^{\bar{G}}$ and
$\mathfrak{g}(\hat{Q})^{\bar{G}}$ as $\mathfrak{g}(\Gamma)$-module is
integrable.

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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph