Finite Dimensional Hopf Algebras Over the Dual Group Algebra of the Symmetric Group in Three Letters

Abstract

We classify finite-dimensional Hopf algebras whose coradical is isomorphic to the algebra of functions on 𝕊₃. We describe a new infinite family of Hopf algebras of dimension 72.

Key Words:

• Algebra of functions on groups
• Hopf algebras whose coradical is a Hopf subalgebra

2000 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENT

N. A. thanks Margaret Beattie for conversations on this problem in St. John's, May 2008.

This work was partially supported by ANPCyT-Foncyt, CONICET, Ministerio de Ciencia y Tecnología (Córdoba) and Secyt (UNC). Part of the work of C. V. was done as a fellow of the Erasmus Mundus programme of the EU in the University of Antwerp. He thanks to Prof. Fred Van Oystaeyen for his warm hospitality and help.

Notes

Communicated by H.-J. Schneider.

Dedicated to Mia Cohen with affection.