comodule coalgebra

Let H be a bialgebraPlanetmathPlanetmathPlanetmath. A right H-comodule coalgebra is a coalgebra A which is a right H-comodule satisfying

(Δid)t(a)=a(1)(1)a(2)(1)a(1)(2)a(2)(2),(εid)t(a)=ε(a)1IH, (1)

for all hH and aA.

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

Example 1

Let H be a Hopf algebraMathworldPlanetmath. Then H is itself a H-comodule coalgebra for the adjointPlanetmathPlanetmath coaction t(h)=h(2)S(h(1))h(3).

Title comodule coalgebra
Canonical name ComoduleCoalgebra
Date of creation 2013-03-22 13:26:39
Last modified on 2013-03-22 13:26:39
Owner mhale (572)
Last modified by mhale (572)
Numerical id 7
Author mhale (572)
Entry type Definition
Classification msc 16W30
Related topic ModuleAlgebra
Related topic ModuleCoalgebra
Related topic ComoduleAlgebra