The Picard Group of Corings

Abstract

We introduce and study the Picard group of a coring. We give an exact sequence relating the Picard group of a coring and its automorphisms generalizing the known exact sequences associated to an algebra and a coalgebra over a field. We also extend to corings the Aut–Pic property and we give some new corings satisfying this property.

Key Words:

• Corings
• The Picard group
• The Aut–Pic property

2000 Mathematics Subject Classification:

• 14C22
• 16W30
• 16W50

ACKNOWLEDGMENTS

I would like to thank my advisor, José Gómez-Torrecillas, for the subject of this article. I am also very grateful to Blas Torrecillas Jover for the helpful discussion. I would also like to thank the referee for some suggestions which allowed me to improve the presentation.

Notes

Communicated by J. L. Gomez Pardo.