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

Subject Areas : Group theory

A. Taha ¹ , M. N. Abdulrahim ²

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

Received: 2018-06-09 Accepted : 2019-03-06 Published : 2019-06-01

Keywords: Braid group, irreducible,

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.

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