The center of the ring of 3×3 generic matrices |
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Authors: | Edward Formanek |
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Institution: |
a The Institute for Advanced Studies, The Hebrew University of Jerusalem, Jerusalem, Israel
b The Pennsylvania State University, University Park, Pennsylvania |
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Abstract: | Following Procesi, the center of the division ring of generic matrices over a field F is described as the fixed field of the symmetric group acting on a purely transcendental extension of F. For 3×3 matrices, the center is shown to be purely transcendental over F. In characteristic zero this is equivalent to saying that the field of simultaneous rational invariants of 3×3 matrices over F is a purely transcendental extension field of F. |
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