Algebras and Representation Theory | 2021
Differential Polynomial Identities of Upper Triangular Matrices Under the Action of the Two-Dimensional Metabelian Lie Algebra
Abstract
We study the differential polynomial identities of the algebra UTm(F) under the derivation action of the two dimensional metabelian Lie algebra, obtaining a generating set of the TL-ideal they constitute. Then we determine the Sn-structure of their proper multilinear spaces and, for the minimal cases m =\u20092, 3, their exact differential codimension sequence.