Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domestic canonical algebras and simple Lie algebras   For each simply-laced Dynkin graph $\Delta$ we realize the simple complex Lie
algebra of type $\Delta$ as a quotient algebra of the complex degenerate
composition Lie algebra $L(A)_{1}^{\mathbb{C}}$ of a domestic canonical algebra
$A$ of type $\Delta$ by some ideal $I$ of $L(A)_{1}^{\mathbb{C}}$ that is
defined via the Hall algebra of $A$, and give an explicit form of $I$.
Moreover, we show that each root space of $L(A)_{1}^{\mathbb{C}}/I$ has a basis
given by the coset of an indecomposable $A$-module $M$ with root easily
computed by the dimension vector of $M$.

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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: q-fin