Domestic canonical algebras and simple Lie algebras
| dc.creator | Asashiba, Hideto | |
| dc.date | 2007-05-07 | |
| dc.date | 2007-06-24 | |
| dc.date.accessioned | 2026-07-07T08:11:46Z | |
| dc.date.available | 2026-07-07T08:11:46Z | |
| dc.description | 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 $M$. | |
| dc.description | 43 pages, 5 figures, revised version | |
| dc.identifier | https://arxiv.org/abs/0705.0942 | |
| dc.identifier | http://arxiv.org/abs/0705.0942 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132229 | |
| dc.subject | Representation Theory | |
| dc.subject | 16G20 | |
| dc.title | Domestic canonical algebras and simple Lie algebras | |
| dc.type | text |