Extension groups for the $C^{\ast }$-algebras associated with $\lambda$-graph systems

A $\lambda$-graph system is a labeled Bratteli diagram with certain additional structure, which presents a subshift. The class of the $C^{\ast }$-algebras ${\mathcal{O}}_{\mathfrak{L}}$ associated with the $\lambda$-graph systems is a generalized class of the class of Cuntz–Krieger algebras. In this paper, we will compute the strong extension groups ${\mathrm{Ext}}_{\mathrm{s}}({\mathcal{O}}_{\mathfrak{L}})$ for the $C^{\ast }$-algebras associated with $\lambda$-graph systems $\mathfrak{L}$ and study their relation with the weak extension group ${\mathrm{Ext}}_{\mathrm{w}}({\mathcal{O}}_{\mathfrak{L}})$.