On comatrix corings and bimodules

To any bimodule that is finitely generated and projective on one side one can associ- ate a coring, known as a comatrix coring. A new description of comatrix corings in terms of data reminiscent of a Morita context is given. It is also studied how properties of bimodules are reflected in the associated comatrix corings. In particular it is shown that separable bimodules give rise to coseparable comatrix corings, while Frobenius bimodules induce Frobenius comatrix corings.

[1]  M. Sweedler,et al.  The predual theorem to the Jacobson-Bourbaki theorem , 1975 .

[2]  L. Kadison Separability and the Twisted Frobenius Bimodule , 1999 .

[3]  S. Majid Foundations of Quantum Group Theory , 1995 .

[4]  Kiiti Morita Adjoint pairs of functors and Frobenius extensions , 1965 .

[5]  Sugano Kozo NOTE ON SEPARABILITY OF ENDOMORPHISM RINGS , 1971 .

[6]  Hyman Bass,et al.  Algebraic K-theory , 1968 .

[7]  Stefaan Caenepeel,et al.  Brauer Groups, Hopf Algebras and Galois Theory , 1998 .

[8]  H. Porst ON CORINGS AND COMODULES , 2003 .

[9]  S. Caenepeel,et al.  FROBENIUS FUNCTORS OF THE SECOND KIND , 2001, math/0106109.

[10]  T. Brzezinski,et al.  Towers of Corings , 2002, math/0201014.

[11]  Robert Wisbauer,et al.  Corings and Comodules , 2003 .

[12]  F. Guzmán Cointegrations, relative cohomology for comodules, and coseparable corings , 1989 .

[13]  S. Caenepeel,et al.  DOI-HOPF MODULES, YETTER-DRINFEL'D MODULES AND FROBENIUS TYPE PROPERTIES , 1997 .

[14]  L. Kadison New Examples of Frobenius Extensions , 1999 .

[15]  José Gómez Torrecillas,et al.  Comatrix corings: Galois corings, descent theory, and a structure theorem for cosemisimple corings: Galois corings, descent theory, and a structure theorem for cosemisimple corings , 2003 .

[16]  Frank W. Anderson,et al.  Rings and Categories of Modules , 1974 .

[17]  Tomasz Brzeziński The Structure of Corings: Induction Functors, Maschke-Type Theorem, and Frobenius and Galois-Type Properties , 2000 .