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Cluster tilting for tilted algebras

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Abstract

We build a connection between iterated tilted algebras with trivial cluster tilting subcategories and tilted algebras of finite type. Moreover, all tilted algebras with cluster tilting subcategories are determined in terms of quivers. As a result, we draw the quivers of Auslander’s 1-Gorenstein algebras with global dimension 2 admitting trivial cluster tilting subcategories, which implies that such algebras are of finite type but not necessarily Nakayama.

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Authors and Affiliations

  1. College of Mathematics and Physics, Nanjing University of Information Science and Techonology, Nanjing, 210044, China

    XiaoJin Zhang

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  1. XiaoJin Zhang
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Correspondence to XiaoJin Zhang.

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Zhang, X. Cluster tilting for tilted algebras. Sci. China Math. 55, 1171–1178 (2012). https://doi.org/10.1007/s11425-011-4330-6

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  • DOI: https://doi.org/10.1007/s11425-011-4330-6

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