module algebra

A **left module $k$-algebra** is a $k$-algebra $A$ equipped with a left Hopf action (also sometimes said module algebra action) $\triangleright: B\otimes A\to A$ of a $k$-bialgebra $B$. 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 $k$-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)