Advances in Operator Theory

Semigroup homomorphisms on matrix algebras

Bernhard Burgstaller

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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.

Article information

Adv. Oper. Theory, Volume 2, Number 3 (2017), 287-292.

Received: 15 February 2017
Accepted: 26 April 2017
First available in Project Euclid: 4 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60] 15B33: Matrices over special rings (quaternions, finite fields, etc.)

semigroup ring matrix multiplicativ additive unique addition $C^*$-algebra


Burgstaller, Bernhard. Semigroup homomorphisms on matrix algebras. Adv. Oper. Theory 2 (2017), no. 3, 287--292. doi:10.22034/aot.1702-1121.

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