Abstract
For each simply-laced Dynkin graph Δ we realize the simple complex Lie algebra of type Δ as a quotient algebra of the complex degenerate composition Lie algebra \(L(A)_{1}^{{\mathbb{C}}}\) of a domestic canonical algebra A of type Δ 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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Dedicated to Professor Claus Michael Ringel on the occasion of his 60th birthday.
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Asashiba, H. Domestic canonical algebras and simple Lie algebras. Math. Z. 259, 713–754 (2008). https://doi.org/10.1007/s00209-007-0246-9
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DOI: https://doi.org/10.1007/s00209-007-0246-9