Generalized reduced Mal'tsev problem on commutative subalgebras of $E_6$ type Chevalley algebras over a field

In 1905 I. Shur pointed out the largest dimension of commutative subgroups in the groups $SL(n,\mathbb{C})$ and proved that for $n>3$ such the subgroups are automorphic to each other. In 1945 A.I. Mal’tsev investigated the problem of description of the largest dimension commutative subgroups in the simple complex Lie groups. He solved the problem by the transition to the complex Lie algebras and by the reduction to the same problem for the maximal nilpotent subalgebra. Let $N$ be a niltriangular subalgebra of a Chevalley algebra. The article deals with the problem of describing the largest dimension commutative subalgebras of $N$ over an arbitrary field. The solution of this problem is obtained for the subalgebra $N$ of $E_6$ type Chevalley algebra.