A class of simple Lie algebras attached to unit forms.

Let n ≥ 3. The complex Lie algebra, which is attached to a unit form q( x , x ,..., x ) = $${\sum\nolimits_{i = 1}^n {x_i^2 + \sum\nolimits_{1 \leqslant i \leqslant j \leqslant n} {\left( { - 1} \right)} } ^{j - i}}{x_i}{x_j}$$ 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 FROM AUTHOR]