2026/07/15 by Fabio Calderón, César Galindo
#math.RA #math.QA
Let H be a strongly G-graded quasi-Hopf algebra, with G an arbitrary group. We classify its quasi-Hopf ideals by showing that each quasi-Hopf ideal I of H corresponds to a pair (N,K), where N is a normal subgroup of G and K is a G/N-invariant quasi-Hopf ideal of HN=\bigoplusn∈ NHn whose image under the grading map contains the augmentation ideal of \Bbbk[N]. We further improve this correspondence for particular classes of quasi-Hopf ideals, such as those that have an associated quasi-Hopf retraction, or those whose lifted quotient is a crossed product. Applications include cocentral abelian extensions with infinite grading, finite neutral component and nontrivial reassociator.