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On Algebras of Finite General Representation Type

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Abstract

We introduce the notion of “finite general representation type” for a finite-dimensional algebra, a property related to the “dense orbit property” introduced by Chindris-Kinser-Weyman. We use an interplay of geometric, combinatorial, and algebraic methods to produce a family of algebras of wild representation type but finite general representation type. For completeness, we also give a short proof that the only local algebras of discrete general representation type are already of finite representation type. We end with a Brauer-Thrall style conjecture for general representations of algebras.

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Acknowledgements

We thank Grzegorz Bobiński, Hipolito Treffinger, Kaveh Mousavand, and Charles Paquette for their comments. We also thank Jenna Rajchgot for the M2 consultation related to Example 4.74. Finally, we appreciate an anonymous referee’s diligent reading and thoughtful suggestions which substantially improved the readability and correctness of the final draft.

Funding

This work was supported by a grant from the Simons Foundation (636534, RK) and by the National Science Foundation under Award No. DMS-2303334.

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  1. University of Iowa, Department of Mathematics, Iowa City, IA, USA

    Ryan Kinser

  2. Texas State University, Department of Mathematics, San Marcos, TX, USA

    Danny Lara

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  1. Ryan Kinser
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Correspondence to Ryan Kinser.

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Kinser, R., Lara, D. On Algebras of Finite General Representation Type. Transformation Groups (2024). https://doi.org/10.1007/s00031-024-09856-1

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