Poisson Hopf algebra related to a twisted quantum group

ABSTRACT

A Poisson algebra ℂ[G] considered as a Poisson version of the twisted quantized coordinate ring ℂ_q,p[G], constructed by Hodges et al. [11], is obtained and its Poisson structure is investigated. This establishes that all Poisson prime and primitive ideals of ℂ[G] are characterized. Further it is shown that ℂ[G] satisfies the Poisson Dixmier-Moeglin equivalence and that Zariski topology on the space of Poisson primitive ideals of ℂ[G] agrees with the quotient topology induced by the natural surjection from the maximal ideal space of ℂ[G] onto the Poisson primitive ideal space.

KEYWORDS:

• Hopf dual
• Poisson Hopf algebra
• Poisson primitive ideal

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B63
• 17B37
• 16W35
• 16D60

Acknowledgment

The author thanks the Korea Institute for Advanced Study for the warm hospitality during a part of the preparation of this paper.