Semigroup homomorphisms on matrix algebras

Document Type: Original Article

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Abstract

We explore the connection between ring homomorphisms and semigroup homomorphisms on matrix algebras over rings or $C^*$-algebras. Further, we give a connection between group homomorphisms on the general linear groups of a matrix stable $C^*$-algebra and their potentially extended homomorphisms on the whole $C^*$-algebra.

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