Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 025, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.025
(Mi sigma1562)
 

Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

Tsukasa Ishibashi

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
References:
Abstract: We give a method to compute presentations of saturated cluster modular groups. Using this, we obtain finite presentations of the saturated cluster modular groups of finite mutation type $X_6$ and $X_7$. We verify that the cluster modular groups of finite mutation type $\widetilde{E}_6$, $\widetilde{E}_7$, $\widetilde{E}_8$, $G_2^{(*,*)}$, $X_6$ and $X_7$ are virtually generated by cluster Dehn twists.
Keywords: cluster algebras, cluster modular groups, mapping class groups, quivers of finite mutation type.
Funding agency Grant number
Japan Society for the Promotion of Science 18J13304
Ministry of Education, Culture, Sports, Science and Technology, Japan Program for Leading Graduate School
This work is partially supported by JSPS KAKENHI Grant Number 18J13304 and the program for Leading Graduate School, MEXT, Japan.
Received: January 1, 2020; in final form March 27, 2020; Published online April 7, 2020
Bibliographic databases:
Document Type: Article
MSC: 13F60, 05E15, 30F60
Language: English
Citation: Tsukasa Ishibashi, “Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists”, SIGMA, 16 (2020), 025, 22 pp.
Citation in format AMSBIB
\Bibitem{Ish20}
\by Tsukasa~Ishibashi
\paper Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists
\jour SIGMA
\yr 2020
\vol 16
\papernumber 025
\totalpages 22
\mathnet{http://mi.mathnet.ru/sigma1562}
\crossref{https://doi.org/10.3842/SIGMA.2020.025}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000528031700001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85084824353}
Linking options:
  • https://www.mathnet.ru/eng/sigma1562
  • https://www.mathnet.ru/eng/sigma/v16/p25
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024