Integrals, quantum Galois extensions and the affineness criterion for quantum Yetter-Drinfel'd modules

Abstract

We introduce and study a general concept of integral of a threetuple (H, A, C), where H is a Hopf algebra acting on a coalgebra C and coacting on an algebra A. In particular, quantum integrals associated to Yetter-Drinfel'd modules are defined. Let A be an H-bicomodule algebra, ${}^H{\mathcal{YD}}_A$ be the category of (generalized) Yetter-Drinfel'd modules and $B$ the subalgebra of coinvariants of the Verma structure of $A$. We introduce the concept of quantum Galois extensions and we prove the affineness criterion in a quantum version.

latex 32 pg. J. Algebra, to appear

References in corpus (2)

• Coalgebra Gauge Theory
• The Long dimodule category and nonlinear equation

Cited by in corpus (1)

• Relative Hom-Hopf modules and total integrals