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arXiv · 1403.0773

The maximal dimension of unital subalgebras of the matrix algebra

A. L. Agore
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Abstract

Using Wederburn's main theorem and a result of Gerstenhaber we prove that, over a field of characteristic zero, the maximal dimension of a proper unital subalgebra in the $n \times n$ matrix algebra is $n^2 - n + 1$ and furthermore this upper bound is attained for the so-called parabolic subalgebras. We also investigate the corresponding notion of parabolic coideals for matrix coalgebras and prove that the minimal dimension of a non-zero coideal of the matrix coalgebra ${\mathcal M}^n (k)$ is $n-1$.

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A. L. Agore. 2014-03-04. The maximal dimension of unital subalgebras of the matrix algebra. https://arxiv.org/abs/1403.0773

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