Domestic canonical algebras and simple Lie algebras

2007/05/07 by Hideto Asashiba, Asashiba, Hideto
Mathematics · Physics and Astronomy · #16G20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:16G20

paper · pdf · doi:10.48550/arxiv.0705.0942

43 pages, 5 figures, revised version

openalex publication_date 2007/05/07 · arxiv created 2007/06/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^ℂ of a domestic canonical algebra A of type Δ by some ideal I of L(A)₁^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^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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