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 27-jul-2024