module coalgebra

Let H be a bialgebraPlanetmathPlanetmath. A left H-module coalgebra is a coalgebra A which is a left H-module with action ha satisfying

Δ(ha)=(h(1)a(1))(h(2)a(2)),ε(ha)=ε(h)ε(a), (1)

for all hH and aA.

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

Example 1

Let H be a bialgebra. Then H is itself a H-module coalgebra for the left regularPlanetmathPlanetmath action gh=gh.

Title module coalgebra
Canonical name ModuleCoalgebra
Date of creation 2013-03-22 13:26:37
Last modified on 2013-03-22 13:26:37
Owner mhale (572)
Last modified by mhale (572)
Numerical id 9
Author mhale (572)
Entry type Definition
Classification msc 16W30
Related topic ComoduleAlgebra
Related topic ModuleAlgebra
Related topic ComoduleCoalgebra