On coideal subalgebras of cocentral Kac algebras and a generalization of Wall's conjecture

TL;DR

This paper investigates the structure of coideal subalgebras within finite-dimensional Hopf algebras, revealing they are cyclic modules over the dual algebra, and classifies these subalgebras in certain cocentral abelian extensions.

Contribution

It introduces a characterization of coideal subalgebras as cyclic modules over the dual Hopf algebra and classifies them in cocentral abelian extensions, extending prior results.

Findings

Coideal subalgebras are cyclic modules over the dual Hopf algebra.

Complete classification of coideal subalgebras in cocentral abelian extensions.

Extends previous results on coideal subalgebras in Hopf algebras.

Abstract

It shown that any coideal subalgebra of a finite dimensional Hopf algebra is a cyclic module over the dual Hopf algebra. Using this we describe all coideal subalgebras of a cocentral abelian extension of Hopf algebras extending some results from [4].