2024-06-17T06:29:55Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/666962024-03-14T20:00:26Zcom_10324_1129com_10324_931com_10324_894col_10324_1193
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Brox, Jose
author
Rizzo, Carla
author
2024
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.
Universidad de Valladolid, Facultad de Ciencias
https://uvadoc.uva.es/handle/10324/66696
Matemáticas
Differential identities of matrix algebras