Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$
محورهای موضوعی : Group theoryA. 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
کلید واژه: Braid group, irreducible,
چکیده مقاله :
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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