A Poisson Hopf algebra related to a twisted quantum group

Abstract

A Poisson algebra $\mathbb{C}[G]$ considered as a Poisson version of the twisted quantized coordinate ring ${\mathbb{C}}_{q,p}[G]$, constructed by Hodges, Levasseur and Toro in \cite{HoLeT}, is obtained and its Poisson structure is investigated. This establishes that all Poisson prime and primitive ideals of $\mathbb{C}[G]$ are characterized. Further it is shown that $\mathbb{C}[G]$ satisfies the Poisson Dixmier-Moeglin equivalence and that Zariski topology on the space of Poisson primitive ideals of $\mathbb{C}[G]$ agrees with the quotient topology induced by the natural surjection from the maximal ideal space of $\mathbb{C}[G]$ onto the Poisson primitive ideal space.

32 pages