We study the equation of state of neutron-star matter including the effects of isovector-vector coupling in quark matter. We employ the relativistic mean-field theory with an extended TM1 parameter set to describe hadronic matter and the SU(3) Nambu-Jona-Lasinio model with isovector-vector and hypercharge-vector couplings to describe the quark matter. The deconfinement hadron-quark phase transition is constructed under Gibbs phase equilibrium conditions. It is found that the isovector-vector and hypercharge-vector couplings in quark matter enhance the symmetry energy and hypercharge symmetry energy in neutron-star matter.
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