module algebra

Let H be a bialgebraPlanetmathPlanetmathPlanetmath. A left H-module algebra is a unital algebraPlanetmathPlanetmathPlanetmath A which is a left H-module with action ha satisfying

h(ab)=(h(1)a)(h(2)b),h1IA=ε(h)1IA, (1)

for all hH and a,bA.

There is a dual notion of a H-comodule coalgebra.

Example 1

Let H be a Hopf algebraMathworldPlanetmath. Then H is itself a H-module algebra for the adjoint action gh=g(1)hS(g(2)).

Title module algebra
Canonical name ModuleAlgebra
Date of creation 2013-03-22 13:26:31
Last modified on 2013-03-22 13:26:31
Owner mhale (572)
Last modified by mhale (572)
Numerical id 8
Author mhale (572)
Entry type Definition
Classification msc 16W30
Related topic ComoduleCoalgebra
Related topic ModuleCoalgebra
Related topic ComoduleAlgebra