Advances in Operator Theory

Semigroup homomorphisms on matrix algebras

Bernhard Burgstaller

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431677

Digital Object Identifier
doi:10.22034/aot.1702-1121

Mathematical Reviews number (MathSciNet)
MR3730055

Zentralblatt MATH identifier
1383.46038

Subjects
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.)

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

Citation

Burgstaller, Bernhard. Semigroup homomorphisms on matrix algebras. Adv. Oper. Theory 2 (2017), no. 3, 287--292. doi:10.22034/aot.1702-1121. https://projecteuclid.org/euclid.aot/1512431677


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