Hopf-Galois algebras and their Poisson structures

2020/05/27 by Zheng, Huihui, Zhang, Liangyun
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2005.13322

Abstract

As is known to all, Hopf-Galois objects have a significant research value for analyzing tensor categories of comodules and classification questions of pointed Hopf algebras, and are natural generalizations of Hopf algebras with a Galois-theoretic flavour. In this paper, we mainly prove a criterion for an Ore extension of a Hopf-Galois algebra to be a Hopf-Galois algebra, and introduce the conception of Poisson Hopf-Galois algebras, and establish the relationship between Poisson Hopf-Galois algebras and Poisson Hopf algebras. Moreover, we study Poisson Hopf-Galois structures on Poisson polynomial algebras, and mainly give a necessary and sufficient condition for the Poisson enveloping algebra of a Poisson Hopf-Galois algebra to be a Hopf-Galois algebra.

Related

• Co-Poisson structures on polynomial Hopf algebras
• Universal enveloping algebras of Poisson Hopf algebras
• Poisson Hopf algebras associated to quantized enveloping algebras
• The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras
• Fundamental theorem of transposed Poisson (A,H)-Hopf modules