Splitting Comodules over Hopf Algebras and Application to Representation Theory of Quantum Groups of Type A0|0

We investigate left and right co-Frobenius coalgebras and give equivalent characterizations which prove statements dual to the characterizations of Frobenius algebras. We prove that a coalgebra is left and right coFrobenius if and only if C ∼ = Rat(C * C * ) as right C * -modules and also that this is equivalent to the fact that the functors Hom K (−, K) and Hom C * (−, C * ) from M C to C * M are isomorphic. This allows a definition of a left-right symmetric concept of co-Frobenius coalgebras that is perfectly dual to the one of Frobenius algebras and coincides to the existing notion left and right co-Frobenius coalgebra.

show abstract

On the dimension of the space of integrals on coalgebras

Dăscălescu

Năstăsescu

Toader

2010

Journal of Algebra

View full text Add to dashboard Cite

We study the injective envelopes of the simple right C -comodules, and their duals, where C is a coalgebra. This is used to give a short proof and to extend a result of Iovanov on the dimension of the space of integrals on coalgebras. We show that if C is right coFrobenius, then the dimension of the space of left M-integrals on C is dim M for any left C -comodule M of finite support, and the dimension of the space of right N-integrals on C is dim N for any right C -comodule N of finite support. Some examples of integrals are computed for incidence coalgebras.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Splitting Comodules over Hopf Algebras and Application to Representation Theory of Quantum Groups of Type A0|0

Cited by 11 publications

References 20 publications

Irreducible representations of quantum linear groups of type A1|0

Irreducible representations of quantum linear groups of type A1|0

Co-Frobenius coalgebras

On the dimension of the space of integrals on coalgebras

Contact Info

Product

Resources

About