Differential identities of matrix algebras

2024/03/14 by Jose Brox, Brox, Jose, Carla Rizzo +1
Computer Science · Mathematics · #15B30 #16G30 #16P90 #16R50 #16S30 #17B10 #17B20 #17B35 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Primary 16R10 #Rings and Algebras (math.RA) #Secondary 16W25

paper · pdf · doi:10.48550/arxiv.2403.09337

openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the differential identities of the algebra M_k(F) of k× k matrices over a field F of characteristic zero when its full Lie algebra of derivations, L=Der(M_k(F)), acts on it. We determine a set of 2 generators of the ideal of differential identities of M_k(F) for k≥ 2. 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 M_k(F) has almost polynomial growth for all k≥ 2.

Related

• Growth of differential identities
• Derived identities of differential algebras
• Matrix identities with forms
• The differential invariants of SL₂(\mathbbF₃) acting on trace-free matrices over \mathbbF₃
• Differentials over differential fields