Poisson Hopf algebra related to a twisted quantum group

A Poisson algebra ?G] considered as a Poisson version of the twisted quantized coordinate ring ?_q,pG], constructed by Hodges et al. 11 Hodges, T. J., Levasseur, T., Toro, M. (1997). Algebraic structure of multi-parameter quantum groups. Adv. Math. 126:52–92.Crossref], Web of Science ®] , Google Scholar]], is obtained and its Poisson structure is investigated. This establishes that all Poisson prime and primitive ideals of ?G] are characterized. Further it is shown that ?G] satisfies the Poisson Dixmier-Moeglin equivalence and that Zariski topology on the space of Poisson primitive ideals of ?G] agrees with the quotient topology induced by the natural surjection from the maximal ideal space of ?G] onto the Poisson primitive ideal space.