Integral theory for left Hopf left bialgebroids

2020/07/18 by Chemla, Sophie · 3 citations
#16S30 #FOS: Mathematics #Rings and Algebras (math.RA) #primary : 16T05 #secundary : 16S10

paper · doi:10.48550/arxiv.2007.09425

Abstract

We study integral theory for left (or right) Hopf left bialgebroids. Contrary to Hopf algebroids, the latter ones don't necessary have an antipode S but, for any element u, the elements u₍₁₎ ⊗ S(u₍₂₎) (or u₍₂₎⊗ S^-1(u₍₁₎) ) does exist. Our results extend those of G. Böhm who studied integral theory for Hopf algebroids. We make use of recent results about left Hopf left bialgebroids. We apply our results to the restricted enveloping algebra of a restricted Lie Rinehart algebra.

Cited by

• Hopf BiGalois Theory for Hopf Algebroids
• Hopf bimodules for bialgebroids
• Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids

Related

• Hopf algebroids with bijective antipodes: axioms, integrals and duals
• An alternative notion of Hopf algebroid
• Integrals for Bialgebras
• Hopf BiGalois Theory for Hopf Algebroids
• Hopf Algebroids, Bimodule Connections and Noncommutative Geometry