Structure of Quantum Doubles of Finite Clifford Monoids

Abstract

In this paper, over a field k, we give the structure theorem of the quantum double of a finite Clifford monoid through bicrossed products and quantum doubles of groups. By this result, it is shown that the quantum double of a finite Clifford monoid is semisimple (resp. von Neumann regular) if and only if the semigroup is a finite group and the characteristic p of k does not divide the order of this group.

Key Words:

• Quantum double
• Clifford semigroup
• Group
• Weak Hopf algebra
• Semisimplicity
• von Neumann regularity

Mathematics Subject Classification:

• 16W35
• 16W30
• 20M25

Acknowledgments

This project (No. 102028) was supported by the Natural Science Foundation of Zhejiang Province. This paper was prepared partly at University of Tasmania in 2000 with the support of an Australia Research Council Grant. The author thanks Prof. Peter Trotter for his kind help. And, he appreciates Dr. David Easdown very much for the effective discussion.

Notes

^#Communicated by E. Zelmanov.