You are here

Home » Content

On the Irreducibility of Perron Representations of Degrees 4 and 5

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2018

Key Words:

Author NameFaculty of Author
Abstract (2. Language): 
We consider the graph En+1;1 with (n+1) generators 1; :::; n, and , where i has an edge with i+1 for i = 1; :::; n+1, and 1 has an edge with . We then de ne the Artin group of the graph En+1;1 for n = 3 and n = 4 and consider its reduced Perron's representation of degrees four and ve respectively. After we specialize the indeterminates used in de ning the representation to non-zero complex numbers, we obtain necessary and sucient conditions that guarantee the irreducibility of the representations for n = 3 and 4 .
Bookmark/Search this post with
FULL TEXT (PDF): 
PDF icon arastirmax-irreducibility-perron-representations-degrees-4-and-5.pdf
  • 1
215
237
  • English

JEL Codes:

REFERENCES

References: 

[1] J. S. Birman, Braids, Links and Mapping Class Groups. Annals of Mathematical Stud-
ies. Princeton University Press, volume 82, New Jersey, 1975.
[2] T.E. Brendle, The Torelli Group and Representations of Mapping Class Groups. Doc-
toral Thesis, Columbia University, 2002.
[3] M. Dally and M. Abdulrahim, On the Irreducibility of Artin's Group of Graphs. Journal
of Mathematics Research, volume 7, number 2, 2015.
[4] V.L. Hansen, Braids and Coverings. London Mathematical Society, Cambridge Uni-
versity Press, 1989.
[5] B. Perron, A linear representaton of a nite rank of the mapping class group of surfaces
(preprint). Laboratoire de Topologie, volume 99, number 204, 1999

Thank you for copying data from http://www.arastirmax.com