nLab
module algebra

A left module kk-algebra is a kk-algebra AA equipped with a left Hopf action (also sometimes said module algebra action) :BAA\triangleright: B\otimes A\to A of a kk-bialgebra BB. Sometimes one talks about module algebras meaning a monoid with Hopf actions of a bimonoid in a more general symmetric monoidal category; a module monoid would be a better term if the category is not kk-linear.

Related entries include smash product algebra, comodule algebra, gebra, bigebra

  • S. Majid, Foundations of quantum group theory, Cambridge University Press 1995, 2000.
  • Susan Montgomery, Hopf algebras and their actions on rings, CBMS Lecture Notes 82, AMS 1993, 240p.
  • Matthew Tucker-Simmons, *\ast-structures on module-algebras, Ph. D. thesis, arxiv/1211.6652

Revised on November 29, 2012 22:08:37 by Zoran Škoda (193.51.104.65)