On Hopf algebras of dimension 4p

Abstract

In this paper, we prove that a non-semisimple Hopf algebra H of dimension 4p with p an odd prime over an algebraically closed field of characteristic zero is pointed provided H contains more than two group-like elements. In particular, we prove that non-semisimple Hopf algebras of dimensions 20, 28 and 44 are pointed or their duals are pointed, and this completes the classification of Hopf algebras in these dimensions.

Reference added, Typos corrected, 22 pages

References in corpus (3)

• Weakly group-theoretical and solvable fusion categories
• Hopf algebras of dimension 2p^2
• Hopf Algebras of Dimension $pq$

Cited by in corpus (7)

• On Classification of Finite-Dimensional Superbialgebras and Hopf Superalgebras
• Classification of connected Hopf algebras of dimension $p^3$ I
• Classification of pointed Hopf algebras of dimension $p^2$ over any algebraically closed field
• Hopf algebras of prime dimension in positive characteristic
• Techniques for classifying Hopf algebras and applications to dimension p^3
• On $4n$-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras
• Quasitriangular Hopf algebras of dimension pq^2