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Artin Group Presentations Arising from Cluster Algebras

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Abstract

In 2003, Fomin and Zelevinsky proved that finite type cluster algebras can be classified by Dynkin diagrams. Then in 2013, Barot and Marsh defined the presentation of a reflection group associated to a Dynkin diagram in terms of an edge-weighted, oriented graph, and proved that this group is invariant (up to isomorphism) under diagram mutations. In this paper, we extend Barot and Marsh’s results to Artin group presentations, defining new generator relations and showing mutation-invariance for these presentations.

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References

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Authors and Affiliations

  1. University of Notre Dame, South Bend, USA

    Jacob Haley

  2. Duke University, Durham, USA

    David Hemminger

  3. Harvard College, Cambridge, USA

    Aaron Landesman

  4. Millikin University, Decatur, USA

    Hailee Peck

Authors
  1. Jacob Haley
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  2. David Hemminger
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  3. Aaron Landesman
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  4. Hailee Peck
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Corresponding author

Correspondence to Jacob Haley.

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Presented by Henning Krause.

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Haley, J., Hemminger, D., Landesman, A. et al. Artin Group Presentations Arising from Cluster Algebras. Algebr Represent Theor 20, 629–653 (2017). https://doi.org/10.1007/s10468-016-9657-9

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  • DOI: https://doi.org/10.1007/s10468-016-9657-9

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