Taha, A., Abdulrahim, M. (2019). Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$. Journal of Linear and Topological Algebra (JLTA), 08(02), 105-115.

A. Taha; M. N. Abdulrahim. "Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$". Journal of Linear and Topological Algebra (JLTA), 08, 02, 2019, 105-115.

Taha, A., Abdulrahim, M. (2019). 'Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$', Journal of Linear and Topological Algebra (JLTA), 08(02), pp. 105-115.

Taha, A., Abdulrahim, M. Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$. Journal of Linear and Topological Algebra (JLTA), 2019; 08(02): 105-115.

Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$

^{1}Department of Mathematics and Computer Science, Beirut Arab University, PO. Box 11-5020, Beirut, Lebanon

^{2}Department of Mathematics and Computer Science, Beirut Arab University, PO. Box 11-5020, Beirut, Lebanon

Abstract

We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$. We specialize the indeterminates used in defining these representations to non zero complex numbers. We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$. We then determine necessary and sufficient conditions that guarantee the irreducibility of the tensor products of the representations of $B_3$. As for the tensor products of the representations of $B_4$, we only find sufficient conditions for the irreducibility of the tensor product.