Aljabar Kumjian-Pask dari Graf-k Berhingga Baris Tanpa Sources
Keywords:
Row-finite K-Graph Without Sources, Kumjian-Pask Algebra, R-Algebra, Quotient, Free R-Algebra, Ideal, Kumjian-Pask RelationsAbstract
Given a row-finite k-graph without sources Λ and a unital commutative ring R. Kumjian-Pask algebra KP_R(Λ) is a universal R-algebra analogous with the graph algebra C*(Λ). For every given Λ, we can construct a Kumjian-Pask algebra KP_R(Λ) as a quotient of free R-algebra on X = Λ^0 ∪ Λ^≠0 ∪ G(Λ^≠0) modulo ideal I generated by a set such that the ideal satisfy Kumjian-Pask relations.
ABSTRAK
Diberikan suatu graf-k berhingga baris tanpa sources Λ dan suatu ring komutatif R dengan unsur kesatuan. Aljabar Kumjian-Pask KP_R(Λ) didefinisikan sebagai aljabar-R universal yang analog dengan aljabar graf C*(Λ). Untuk setiap Λ yang diberikan, dapat dikonstruksi aljabar Kumjian-Pask KP_R(Λ) sebagai kuosien dari aljabar-R bebas pada X = Λ^0 ∪ Λ^≠0 ∪ G(Λ^≠0) modulo ideal I yang dibangun oleh suatu himpunan sedemikian sehingga memenuhi relasi Kumjian-Pask.
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