Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Abdulrahim, Mohammad N."'
We use $q$-Pascal's triangle to define a family of representations of dimension 6 of the braid group $B_3$ on three strings. Then we give a necessary and sufficient condition for these representations to be irreducible.
Externí odkaz:
http://arxiv.org/abs/2304.02304
This work discusses the open problem of the faithfulness of the reduced Burau representation for $n=4$. Birman showed that in order to prove this representation is faithful, it is sufficient to find two matrices $A$ and $B$ that generate a free group
Externí odkaz:
http://arxiv.org/abs/2204.03907
Let $C_n$ be the group of conjugating automorphisms. We study the representation $\rho$ of $C_n$, an extension of Lawrence-Krammer representation of the braid group $B_n$, defined by Valerij G. Bardakov. As Bardakov proved that the representation $\r
Externí odkaz:
http://arxiv.org/abs/2109.13501
We construct a family of six dimensional block representations of the braid group $B_3$ on three strings. We show that some of these representations can be used to detect braid vertibility of some known knots and others of 9 and 10 crossings.
Externí odkaz:
http://arxiv.org/abs/2109.12646
We consider the irreducible representations each of dimension 2 of the necklace braid group $\mathcal{NB}_n$ ($n=2,3,4$). We then consider the tensor product of the representations of $\mathcal{NB}_n$ ($n=2,3,4$) and determine necessary and sufficien
Externí odkaz:
http://arxiv.org/abs/2010.13113
We study the $n$th degree representations $\hat{\rho_G}$ of $Cb_{n}$ and $\hat{\rho_B}$ of $C_{n}$, defined by Valerij G. Bardakov, where $Cb_{n}$ is the group of basis conjugating automorphisms and $C_n$ is the group of conjugating automorphisms. We
Externí odkaz:
http://arxiv.org/abs/2010.09093
We consider Albeverio- Rabanovich linear representation $\pi$ of the braid group $B_3$. After specializing the indeterminates used in defining the representation to non-zero complex numbers, we prove that the restriction of $\pi$ to the pure braid gr
Externí odkaz:
http://arxiv.org/abs/1910.04714
We consider a 2-dimensional representation of the Hecke algebra $\mathcal{H}(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u=(x_1, x_2, y_1, y_2, y_3, z_1, z_2, z_3)$. After specializing the indetrminates
Externí odkaz:
http://arxiv.org/abs/1609.03192
Autor:
Kahil, Rana S.1 (AUTHOR), Abdulrahim, Mohammad N.1 (AUTHOR) mna@bau.edu.lb
Publikováno v:
Arabian Journal of Mathematics. Aug2022, Vol. 11 Issue 2, p303-311. 9p.
Autor:
Mayassi, Taher I.1 tim187@student.bau.edu.lb, Abdulrahim, Mohammad N.1 mna@bau.edu.lb
Publikováno v:
Note di Matematica. 2022, Vol. 42 Issue 2, p53-62. 10p.