On semiprojectivity of 𝐶*-algebras of directed graphs

Abstract

It is shown that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding="application/x-tex">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a countable, transitive directed graph with finitely many vertices, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript asterisk Baseline left-parenthesis upper E right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">C^*(E)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is semiprojective.