ON THE FAITHFULNESS OF JONES-WENZL
REPRESENTATION OF THE BRAID GROUP B4
Malak M. Dally1, Mohammad N. Abdulrahim2
1,2 Department of Mathematics
Beirut Arab University
P.O. Box 11-5020, Beirut, LEBANON

Abstract

We consider the Jones-Wenzl representation $\rho_{4}^{(k,r)}$ of the braid group $B_{4}$. For each pair of integers (k,r) with $r \geq k+1$, we exclude a family of words in the generators from belonging to the kernel of $\rho_{4}^{(k,r)}$. Then, we prove that $\rho_{4}^{(k,r)}$ is not faithful for any even integer $r$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 3
Year: 2019

DOI: 10.12732/ijam.v32i3.4

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References

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