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

Journal of Linear and Topological Algebra

مقاله 3، دوره 08، شماره 02، شهریور 2019، صفحه 105-115   

نوع مقاله: Research Paper

نویسندگان

A. Taha¹؛ M. N. Abdulrahim^{* 2}

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

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

چکیده

‎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.
 

کلیدواژه‌ها

Braid group؛ irreducible

مراجع

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