Prime and primitive Kumjian-Pask algebras

2015/12/02 by Kashoul-Radjabzadeh, Maryam, Larki, Hossein, Aminpour, Abdolmohammad
#16L05 #16W50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1512.00797

Abstract

In this paper, prime as well as primitive Kumjian-Pask algebras KP_R(Λ) of a row-finite k-graph Λ over a unital commutative ring R are completely characterized in graph-theoretic and algebraic terms. By applying quotient k-graphs, these results describe prime and primitive graded basic ideals of Kumjian-Pask algebras. In particular, when Λ is strongly aperiodic and R is a field, all prime and primitive ideals of a Kumjian-Pask algebra KP_R(Λ) are determined.

Related

• Purely infinite simple Kumjian-Pask algebras
• The socle and semisimplicity of a Kumjian-Pask algebra
• Higher-rank graphs and the graded K-theory of Kumjian-Pask Algebras
• Kumjian-Pask algebras of higher-rank graphs
• Simple modules for Kumjian-Pask algebras