C^*-algebras generated by the paths semigroup

2016/08/06 by Grigoryan, Suren, Grigoryan, Tamara, Lipacheva, Ekaterina +1
#46L05 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1608.02086

Abstract

In this paper we study the structure of the C^*-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic C^*-algebras over this poset. We construct the extensions of this algebra, such that the algebra is an ideal in that extensions and quotient algebras are isomorphic to the Cuntz algebra.

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