摘要
Abstract Let n ≥ 3. The complex Lie algebra, which is attached to a unit form xixj and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A~, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra of radical square zero. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra.
Abstract Let n ≥ 3. The complex Lie algebra, which is attached to a unit form xixj and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A~, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra of radical square zero. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra.
