Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T04:49:04.400Z Has data issue: false hasContentIssue false
  • English
  • Français

ASYMPTOTIC TRIANGULATIONS AND COXETER TRANSFORMATIONS OF THE ANNULUS

Part of: Representation theory of rings and algebras Arithmetic rings and other special rings Special aspects of infinite or finite groups

Published online by Cambridge University Press:  27 February 2017

HANNAH VOGEL ,
ANNA FELIKSON  and
PAVEL TUMARKIN
HANNAH VOGEL
Affiliation:
NAWI Graz, Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria e-mail: hannah.vogel@uni-graz.at
ANNA FELIKSON
Affiliation:
Department of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, United Kingdom e-mails: anna.felikson@durham.ac.uk, pavel.tumarkin@durham.ac.uk
PAVEL TUMARKIN
Affiliation:
Department of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, United Kingdom e-mails: anna.felikson@durham.ac.uk, pavel.tumarkin@durham.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Asymptotic triangulations can be viewed as limits of triangulations under the action of the mapping class group. In the case of the annulus, such triangulations have been introduced in K. Baur and G. Dupont (Compactifying exchange graphs: Annuli and tubes, Ann. Comb.3(18) (2014), 797–839). We construct an alternative method of obtaining these asymptotic triangulations using Coxeter transformations. This provides us with an algebraic and combinatorial framework for studying these limits via the associated quivers.

MSC classification

Primary: 16G20: Representations of quivers and partially ordered sets
Secondary: 20F55: Reflection and Coxeter groups 13F60: Cluster algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 63 - 96
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

REFERENCES

1. Bastian, J., Mutation classes of Ãn -quivers and derived equivalence classification of cluster tilted algebras of type Ãn , Algebra Number Theory 5 (5) (2011), 567–594.Google Scholar
2. Baur, K. and Dupont, G., Compactifying exchange graphs: Annuli and tubes, Ann. Comb. 3 (18) (2014), 797–839.Google Scholar
3. Baur, K. and Marsh, R. J., A geometric model of tube categories, J. Algebra 362 (2012), 178–191.Google Scholar
4. Derksen, H., Weyman, J. and Zelevinsky, A., Quivers with potentials and their representations I: Mutations, Sel. Math. 2 (14) (2008), 59–119.Google Scholar
5. Fomin, S. and Zelevinsky, A., Cluster algebras I. Foundations, J. Amer. Math. Soc. 2 (15) (2002), 497–529.Google Scholar
6. Hatcher, A., On triangulations of surfaces, Topology Appl. 40 (2) (1991), 189–194.CrossRefGoogle Scholar
7. Krause, H., Representations of quivers via reflection functors, arXiv:0804.1428, (2008).Google Scholar
8. Labardini-Fragoso, D., On triangulations, quivers with potentials and mutations, Mexican Mathematicians Abroad 657 (2016), 103.Google Scholar