Published 2024-01-01
“…In this paper, we study the tilting quiver of <i>A</i> from the viewpoint of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>-
tilting theory. First, we prove that there exists an isomorphism between the support <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>-tilting quiver <i>Q</i>(s<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>-tilt <i>A</i>) of <i>A</i> and the tilting quiver <i>Q</i>(tilt <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>A</mi><mo>¯</mo></mover></semantics></math></inline-formula>) of the duplicated algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>A</mi><mo>¯</mo></mover></semantics></math></inline-formula>. …”
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