comodule algebra

Let H be a bialgebraPlanetmathPlanetmath. A right H-comodule algebra is a unital algebraPlanetmathPlanetmath A which is a right H-comodule satisfying

t(ab)=t(a)t(b)=a(1)b(1)a(2)b(2),t(1IA)=1IA1IH, (1)

for all hH and a,bA.

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

Example 1

Let H be a bialgebra. Then H is itself a H-comodule algebra for the right regular coaction t(h)=Δ(h).

Title comodule algebra
Canonical name ComoduleAlgebra
Date of creation 2013-03-22 13:26:34
Last modified on 2013-03-22 13:26:34
Owner mhale (572)
Last modified by mhale (572)
Numerical id 8
Author mhale (572)
Entry type Definition
Classification msc 16W30
Related topic ModuleCoalgebra
Related topic ModuleAlgebra
Related topic ComoduleCoalgebra