We study the duality between corings and ring extensions. We construct a new category with a self-dual functor acting on it, which extends that duality. This construction can be seen as the non-commutative case of another duality extension: the duality between finite dimensional algebras and coalgebra. Both these duality extensions have some similarities with the Pontryagin-van Kampen duality theorem.
References
[1]
Morris, S.A. Pontryagin Duality and the Structure of Locally Compact Abelian Groups; Cambridge University Press: Cambridge, UK, 1977.
[2]
Nichita, F.F.; Schack, S.D. The duality between algebras and coalgebras. Ann. Univ. Ferrara -Sez. VII -Sc. Mat. 2005, 51, 173–181.
[3]
Brzeziński, T.; Wisbauer, R. Corings and Comodules; Cambridge University Press: Cambridge, UK, 2003.
[4]
Nichita, F.F. Algebraic models for transdisciplinarity. Transdiscipl. J. Eng. Sci. 2011, 10, 42–46.
[5]
Abe, E. Hopf Algebras; Cambridge University Press: Cambridge, UK, 1977.
[6]
D？sc？lescu, S.; N？st？sescu, C.; Raianu, S. Hopf Algebras: An Introduction; Marcel Dekker, Inc.: New York, NY, USA, 2000.
[7]
Sweedler, M.E. Hopf Algebras; W.A.Benjamin, Inc.: New York, NY, USA, 1969.
[8]
Sweedler, M.E. The predual theorem to the Jacobson-Bourbaki theorem. Trans. Am. Math. Soc. 1975, 213, 391–406, doi:10.1090/S0002-9947-1975-0387345-9.
[9]
Kassel, C. Quantum Groups; Springer Verlag: New York, NY, USA, 1995.
[10]
Lambe, L.; Radford, D. Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach; Kluwer Academic Publishers: Dordrecht, Germany, 1997.
[11]
Nichita, F.F. Non-Linear Equation, Quantum Groups and Duality TheoremsPh.D. Thesis, The State University of New York at Buffalo, 2001.
[12]
Nichita, F.F. Self-inverse Yang-Baxter operators from (co)algebra structures. J. Algebra 1999, 218, 738–759.
