RT info:eu-repo/semantics/article T1 Differential identities of matrix algebras A1 Brox, Jose A1 Rizzo, Carla K1 Matemáticas K1 polynomial identity, differential identity, matrix algebra, universal enveloping algebra, variety of algebras, codimension growth, cocharacter K1 1201.11 Teoría de Matrices K1 1201.13 Polinomios K1 1201.05 Campos, Anillos, Álgebras K1 1201.09 Álgebra de Lie AB We study the differential identities of the algebra Mk(F) of k x k matrices over a field F of characteristic zero when its full Lie algebra of derivations, L=Der(Mk(F)), acts on it. We determine a set of 2 generators of the ideal of differential identities of Mk(F) for k>1. Moreover, we obtain the exact values of the corresponding differential codimensions and differential cocharacters. Finally we prove that, unlike the ordinary case, the variety of differential algebras with L-action generated by Mk(F) has almost polynomial growth for all k>1. PB Universidad de Valladolid, Facultad de Ciencias YR 2024 FD 2024 LK https://uvadoc.uva.es/handle/10324/66696 UL https://uvadoc.uva.es/handle/10324/66696 LA eng NO Universidad de Valladolid, Facultad de Ciencias NO Producción Científica DS UVaDOC RD 11-jul-2024