Products of Linear Maps on Bialgebras, with Applications to Left Hopf Algebras and Hopf Algebroids

Abstract

The Doi–Koppinen generalized smash product can be applied to linear maps on bialgebras, and we define a new associative product for linear maps on bialgebras. We comment on the applications of these products to left Hopf algebras and Hopf algebroids.

Key Words:

• Bialgebra
• Left Hopf algebra
• Smash product

Mathematics Subject Classification:

• Primary 16W30
• Secondary 16S40

ACKNOWLEDGMENTS

The authors would like to thank T. Brzeziński (Swansea) for useful comments.

Notes

Communicated by M. Cohen.