Field of Borel Group Invariant of adjoint representatnion of the group GL(n, K)

Abstract

The paper is devoted to invariant theory problems. In particular, to the problem of finding generators of invariant fields in an explicit form. The set of generators is given for invariant field of unitriangular group of adjoint representation of $GL(n,K)$. Moreover, the set of generators of borel group invariant field is constructed and their algebraic independence is proved. Keywords: Lie group, adjoint representation, the field of invariant, generators of the field of invariant, Borel group.