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

Abstract

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