# A quotient of the braid group related to pseudosymmetric braided categories - Mathematics > Quantum Algebra

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Abstract: Motivated by the recently introduced concept of a pseudosymmetric braidedmonoidal category, we define the pseudosymmetric group PS n, as the quotient ofthe braid group B n by the relations \sigma i\sigma {i+1}^{-1}\sigma i=\sigma {i+1}\sigma i^{-1}\sigma {i+1}, with 1\leq i\leq n-2. It turns out that PS nis isomorphic to the quotient of B n by the commutator subgroup P n, P n ofthe pure braid group P n which amounts to saying that P n, P n coincideswith the normal subgroup of B n generated by the elements \sigma i^2,\sigma {i+1}^2, with 1\leq i\leq n-2, and that PS n is a linear group.

Author: ** Florin Panaite, Mihai D. Staic**

Source: https://arxiv.org/