On the sum of the dimension of a matrix subalgebra and its centralizer

Details On the sum of the dimension of a matrix subalgebra and its centralizer On the sum of the dimension of a matrix subalgebra and its centralizer

2009-12-24

arxiv.org/abs/0912.4821v2

Mathematics

Rings and Algebras

17 pages (withdrawn as it appears there is a much shorter proof available)

Scientific paper

When $\mathbb{K}$ is a field, and $\mathcal{A}$ and $\mathcal{B}$ denote
commuting subspaces of $\text{M}_n(\K)$ each of which contains a non-scalar
matrix, we prove that $\dim \mathcal{A} +\dim \mathcal{B} \leq (n-1)^2+3$. We
also give a complete description of the cases when equality holds.

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