Sira Gratz

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20182022

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math.RT2022

Cluster structures for the $A_{\infty}$ singularity

Jenny August, Man-Wai Cheung, Eleonore Faber +2

We study a category $C_{2}$ of $Z$ -graded MCM modules over the $A_{\infty}$ curve singularity and demonstrate it has infinite type $A$ cluster combinatorics. In part…

math.RT2019

Cluster tilting modules for mesh algebras

Karin Erdmann, Sira Gratz, Lisa Lamberti

We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid…

Cluster structures for the A∞​ singularity

Cluster tilting modules for mesh algebras

Cluster structures for the $A_{\infty}$ singularity