Matrix semigroup homomorphisms into higher dimensions |
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Authors: | Damjana Kokol Bukovšek |
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Institution: | Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia |
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Abstract: | We study non-degenerate irreducible homomorphisms from the multiplicative semigroup of all n-by-n matrices over an algebraically closed field of characteristic zero to the semigroup of m-by-m matrices over the same field. We prove that every non-degenerate homomorphism from the multiplicative semigroup of all n-by-n matrices to the semigroup of (n + 1)-by-(n + 1) matrices when n ? 3 is reducible and that every non-degenerate homomorphism from the multiplicative semigroup of all 3-by-3 matrices to the semigroup of 5-by-5 matrices is reducible. |
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Keywords: | Matrix semigroup Semigroup homomorphism Multiplicative map Irreducibility |
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