Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The maximal dimension of unital subalgebras of the matrix algebra   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 $n-1$.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
16
The categories of this paper are: stat