A Family of Maximal Mathieu Subspaces of Matrix Algebras

2022/06/02 by George F. Seelinger, Wenhua Zhao, Seelinger, George F. +1
Mathematics · #16D99 #16P10 #16P99 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2206.01248

openalex publication_date 2022/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a field. In this note we give a construction for a family of maximal Mathieu subspaces (or Mathieu-Zhao subspaces) of the matrix algebras M_n(F) (n≥ 2). As an application we also give a classification of Mathieu subspaces of M₂(F) under the condition that F is algebraically closed.

Related

• Mathieu-Zhao spaces of polynomial rings
• Multiplicative maps on matrix algebras
• Affine subspaces of units in simple algebras
• Classification of certain types of maximal matrix subalgebras
• The classification of large spaces of matrices with bounded rank