Mathieu subspaces of codimension less than n of Mat_n(K)

Abstract

We classify all Mathieu subspaces of ${\mathrm{Mat}}_n(K)$ of codimension less than $n$, under the assumption that $\mathrm{char}K=0$ or $\mathrm{char}K\ge n$. More precisely, we show that any proper Mathieu subspace of ${\mathrm{Mat}}_n(K)$ of codimension less than $n$ is a subspace of $\{M\in {\mathrm{Mat}}_n(K)\mid \mathrm{tr}M=0\}$ if $\mathrm{char}K=0$ or $\mathrm{char}K\ge n$. On the other hand, we show that every subspace of $\{M\in {\mathrm{Mat}}_n(K)\mid \mathrm{tr}M=0\}$ of codimension less than $n$ in ${\mathrm{Mat}}_n(K)$ is a Mathieu subspace of ${\mathrm{Mat}}_n(K)$ if $\mathrm{char}K=0$ or $\mathrm{char}K\ge n+1$.

20 pages

References in corpus (2)

• The Amazing Image Conjecture
• A Generalization of Mathieu Subspaces to Modules of Associative Algebras

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