On Hopf algebras over the unique 12-dimensional Hopf algebra without the dual Chevalley property. Issue 4 (3rd April 2019)

• Record Type: Journal Article
• Authors: Xiong, Rongchuan
• Is Part Of: Communications in algebra. Volume 47:Issue 4(2019)
• Page Start: 1516
• Page End: 1540
• Publication Date: 2019-04-03
• Subjects: Generalized lifting method -- Hopf algebra -- Nichols algebra; 16T05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1508582
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let k be an algebraically closed field of characteristic zero. We determine all finite-dimensional Hopf algebras over k whose Hopf coradical is isomorphic to the unique 12-dimensional Hopf algebra C without the dual Chevalley property, such that the diagrams are strictly graded and the corresponding infinitesimal braidings are indecomposable objects in C C Y D . In particular, we obtain new Nichols algebras of dimension 18 and 36 and two families of new Hopf algebras of dimension 216.