Abstract
For given bound quiver algebras A and B, we obtain a new algebra Λ, called the simple gluing algebra, by identifying two vertices. We investigate the Gorenstein homological property, the singularity category, the Gorenstein defect category and the Cohen-Macaulay Auslander algebra of Λ in terms of that of A and B. Finally, we give applications to cluster-tilted algebras.
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Acknowledgments
The work was done during the stay of the author at the Department of Mathematics, University of Bielefeld. He is deeply indebted to Professor Henning Krause for his kind hospitality, inspiration and continuous encouragement. The author thanks Professor Liangang Peng very much for his guidance and constant support. The author was supported by the National Natural Science Foundation of China (No. 11401401 and No. 11601441).
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Presented by: Steffen Koenig
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Lu, M. Gorenstein Properties of Simple Gluing Algebras. Algebr Represent Theor 22, 517–543 (2019). https://doi.org/10.1007/s10468-018-9782-8
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DOI: https://doi.org/10.1007/s10468-018-9782-8