Title: Realization of Simple Lie Algebras Via Hall Algebras of Tubular Algebras
Abstract: In recent years,representation theory of finite-dimensional algebras has intersected and permeated through Lie algebras,which is one of the important features.It is an interesting problem on realization of Lie algebras via Hall algebras.According to Asashiba,it takes advantage of the isomorphic correspondance between Ringel-Hall Lie algebras which are realized by root categories of Tubular algebras and 2-Toroidal Lie algebras to construct quotient algebras of degenerate composition Lie algebras of Tubular algebras of type T_((2,2,2,2)),T_((3,3,3)),T_((4,4,2)),T_((6,3,2)).They are proved to be isomorphic to complex simple Lie algebras of type D_4,E_6,E_7,E_8.Moreover the Lie bracket is only given by the Hall multiplication.Then it is given an explicit realization of simple Lie algebras of type D_4 by computing the coefficients.
Publication Year: 2006
Publication Date: 2006-01-01
Language: en
Type: article
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