Tilting objects with higher representation infinite endomorphism rings and strict root pairs are constructed for two families of toric singularities, giving cluster equivalences and explicit Calabi-Yau algebras.
Amiot, Cluster categories for algebras of global dime nsion 2 and quivers with potentional, Ann
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Higher hereditary algebras and Calabi-Yau algebras arising from some toric singularities
Tilting objects with higher representation infinite endomorphism rings and strict root pairs are constructed for two families of toric singularities, giving cluster equivalences and explicit Calabi-Yau algebras.