Левосимметрические структуры на нильтреугольных алгебрах Шевалле

We prove that the algebra N T (n, K) of lower niltriangular n × n matrices over a field K is the unique associative exact enveloping algebra of the niltriangular subalgebra N Φ(K) of the Chevalley algebra of type An−1 that admits a grading compatible with the Cartan grading. We also construct graded left-symmetric structures on the algebras N Φ(K) of classical types Bn, Cn, and Dn