A Poisson Hopf algebra related to a twisted quantum group

TL;DR

This paper constructs a Poisson algebra as a classical limit of a twisted quantum group, characterizes its Poisson prime and primitive ideals, and demonstrates it satisfies the Poisson Dixmier-Moeglin equivalence.

Contribution

It introduces a Poisson algebra related to a twisted quantum group and analyzes its ideal structure and topological properties.

Findings

All Poisson prime and primitive ideals are characterized.

The algebra satisfies the Poisson Dixmier-Moeglin equivalence.

Zariski topology matches the quotient topology on primitive ideals.

Abstract

A Poisson algebra $\Bbb C[G]$ considered as a Poisson version of the twisted quantized coordinate ring $\Bbb C_{q,p}[G]$, 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 $\Bbb C[G]$ are characterized. Further it is shown that $\Bbb C[G]$ satisfies the Poisson Dixmier-Moeglin equivalence and that Zariski topology on the space of Poisson primitive ideals of $\Bbb C[G]$ agrees with the quotient topology induced by the natural surjection from the maximal ideal space of $\Bbb C[G]$ onto the Poisson primitive ideal space.