C^*-ALGEBRAS OF SOME SEMIGROUPS

Abstract

In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.

Keywords

• Left regular representation;
• cyclic representation;
• universal representation;
• reduced $C^*$-algebra and full $C^*$-algebra of a group

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Acknowledgement

Supported by : Chungbuk National University

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