The Niltriangular Subalgebra of the Chevalley Algebra: the Enveloping Algebra, Ideals, and Automorphisms.

The enveloping algebra of the niltriangular subalgebra <italic>N</italic>Φ(<italic>K</italic>) of the Chevalley algebra of type <italic>A</italic><italic>n</italic>−1 is the algebra of niltriangular <italic>n</italic> × <italic>n</italic> matrices over <italic>K</italic>. The enveloping algebras <italic>R</italic> of other types constructed so far are nonassociative. For classical types, an explicit description of automorphisms of the rings <italic>R</italic> over any commutative associative ring with an identity is given; in the case where <italic>K</italic> is a field, all ideals in <italic>R</italic> are also listed. The enumeration of ideals in <italic>R</italic> for <italic>K</italic> = <italic>GF(q)</italic> leads to a solution of a combinatorial problem concerning ideals of the algebras <italic>N</italic>Φ(<italic>K</italic>). [ABSTRACT FROM AUTHOR]