%0 Journal Article
%T Domestic canonical algebras and simple Lie algebras
%A Hideto Asashiba
%J Mathematics
%D 2007
%I arXiv
%X 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 $M$.
%U http://arxiv.org/abs/0705.0942v4