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A computing strategy and programs to resolve the Gerstenhaber Problem for commuting triples of matrices
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A computing strategy and programs to resolve the Gerstenhaber Problem for commuting triples of matrices
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A computing strategy and programs to resolve the Gerstenhaber Problem for commuting triples of matrices
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Paper
A computing strategy and programs to resolve the Gerstenhaber Problem for commuting triples of matrices
2020
Overview
We describe a MATLAB program that could produce a negative answer to the Gerstenhaber Problem by the construction of three commuting \\(n n\\) matrices \\(A,B,C\\) over a field \\(F\\) such that the subalgebra \\(F[A,B,C]\\) they generate has dimension greater than \\(n\\). This problem has remained open for nearly 60 years, following Gerstenhaber's surprising result (Annals Math.) that \\( F[A,B] n\\) for any two commuting matrices \\(A,B\\). The property fails for four or more commuting matrices. We also make the MATLAB files freely available.
