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A class of representations of Artin braid hypergroups

M. Al Tahan

Department of Mathematics, Lebanese International University, Lebanon

E-mail Address: madeline.tahan@liu.edu.lb

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and

B. Davvaz

Department of Mathematics, Yazd University, Yazd, Iran

E-mail Address: davvaz@yazd.ac.ir

Corresponding author.

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https://doi.org/10.1142/S1793557120500564Cited by:0 (Source: Crossref)

Abstract

Hypergroup is the generalized concept of group introduced first by Marty. Since then, the study of it and its applications has been of great importance. This paper deals with representations of the hypergroup associated to the braid group $B_{n}$ $B_{n}$ . First, we define our hypergroup $(B_{n}, ⋆)$ $(B_{n}, ⋆)$ and our semihyperring $(P, \oplus, ⊙)$ $(P, \oplus, ⊙)$ over the set of non-negative integers. Next, we construct non-trivial matrix representations of $B_{n}$ $B_{n}$ of degree $k$ $k$ , for all $k \in ℕ$ . Finally, we find all matrix representations of $(B_{n}, ⋆)$ with degree less than $3$ and classify them according to irreducibility and unitarizability.

Communicated by P. Corsini

Keywords:

AMSC: 17B10, 20F36, 20N20

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