Classification of tight \(C^*\)-algebras over the one-point compactification of \(\mathbb N\)

Abstract: We prove a strong classification result for a certain class of

C^{*}

-algebras with primitive ideal space

w i d e t i l d e m a t h b b N

, where

w i d e t i l d e m a t h b b N

is the one-point compactification of

m a t h b b N

. This class contains the class of graph

C^{*}

-algebras with primitive ideal space

w i d e t i l d e m a t h b b N

. Along the way, we prove a universal coefficient theorem with ideal-related

K

-theory for

C^{*}

-algebras over

w i d e t i l d e m a t h b b N

whose

i n f t y

fiber has torsion-free

K

-theory.