Leavitt path algebras with coefficients in a Clifford semifield

Abstract

In this article, we define the Leavitt path algebra $L_S(\Gamma )$ of a directed graph Γ with coefficients in a Clifford semifield S. The general properties of $L_S(\Gamma )$ are briefly discussed. Then, concentrating on the full k-simplicity (that is, the property of having no nontrivial full k-ideals), we find the necessary and sufficient condition for full k-simplicity of $L_S(\Gamma )$ of a directed graph Γ over a Clifford semifield S. Also, we introduce c-homomorphisms of Leavitt path algebras over Clifford semifields and establish a version of the (Cuntz-Krieger) Uniqueness theorem for the Clifford semifield setting.

Keywords:

• Leavitt path algebra
• semiring
• additive inverse semiring
• Clifford semifield
• full k-simplicity
• Cuntz–Krieger uniqueness theorem

2010 Mathematics Subject Classification:

• 16Y60
• 16D99
• 16D25
• 16G99
• 16S10

Acknowledgements

The authors are grateful to the referee for the valuable suggestions which have definitely enriched the article.

Disclosure statement

No potential conflict of interest was reported by the authors.