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Figure from:Classification of Leavitt Path Algebras with Gelfand-Kirillov Dimension <4 up to Morita Equivalence

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The complete reduction [3 of the digraph I above does not depend on the choice of reductions. However, complete reductions are not unique (up to di graph isomorphism) in general. For instance, the digraph A below has tw« non-isomorphic complete reductions:

Figure 1 The complete reduction [3 of the digraph I above does not depend on the choice of reductions. However, complete reductions are not unique (up to di graph isomorphism) in general. For instance, the digraph A below has tw« non-isomorphic complete reductions:

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Examples 26 The graph C*-algebras of the following digraphs (which are the completions of Leavitt path algebras with complex coefficients) are quantum disks, quantum spheres and quantum real projective spaces [14]. The graph C*- algebra of qD?, the quantum 2-disk is also the Toeplitz algebra, the Leavitt path algebra of this digraph is isomorphic to the Jacobson algebra F(x, y)/(1 — xy).
Examples 26 The graph C*-algebras of the following digraphs (which are the completions of Leavitt path algebras with complex coefficients) are quantum disks, quantum spheres and quantum real projective spaces [14]. The graph C*- algebra of qD?, the quantum 2-disk is also the Toeplitz algebra, the Leavitt path algebra of this digraph is isomorphic to the Jacobson algebra F(x, y)/(1 — xy).
Note that GK dimLy(T) = ht(T) is the dimension of the quantum space for these digraphs.
Note that GK dimLy(T) = ht(T) is the dimension of the quantum space for these digraphs.