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Lecture notes on quivers with superpotential and their representations

  • Special Section: Geometry in Algebra and Algebra in Geometry
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Abstract

These lecture notes are based on a mini-course presented at the fifth version of the Workshop Geometry in Algebra and Algebra in Geometry held in Medellín–Colombia in October 2019. The aim is to provide the background necessary to understand the theory of quivers with relations given by superpotentials. A heavy emphasis is placed throughout on examples to illustrate the applicability of the theory. The motivations for the lectures come from several sources: superpotentials in physics, Calabi–Yau algebras, and noncommutative resolutions.

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Acknowledgements

A.Q.V. is cordially thankful to the Organizing Committee of GAAG-V for the opportunity to present these results to the audience and providing him the conditions that made possible the writing of these lecture notes in a proper way. F.V. is thankful for the partial support given by CODI, Universidad de Antioquia, Project 2017-15756 Stable Limit Linear Series on Curves. F.V. is also grateful for the support given by the Network NT8 for Geometry and Physics from the Office of External Activities, ICTP, which allowed him to attend the event GAAG-V. Both, the event GAAG-V and the writing, were partially supported by CODI, Universidad de Antioquia, Project 2017-15756 Stable Limit Linear Series on Curves.

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Authors and Affiliations

  1. Escuela de Matemáticas, Universidad Nacional de Colombia Sede Medellín, Carrera 65 # 59A–110, Medellín, Colombia

    Alexander Quintero Vélez

  2. Instituto de Matemáticas, Universidad de Antioquia, Calle 70 # 52–21, Medellín, Colombia

    Fabricio Valencia

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  1. Alexander Quintero Vélez
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  2. Fabricio Valencia
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Correspondence to Alexander Quintero Vélez.

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Communicated by Pedro Hernandez Rizzo.

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Quintero Vélez, A., Valencia, F. Lecture notes on quivers with superpotential and their representations. São Paulo J. Math. Sci. 15, 720–743 (2021). https://doi.org/10.1007/s40863-020-00192-2

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