Frobenius algebras of corepresentations and group-graded vector spaces

Abstract We consider Frobenius algebras in the monoidal category of right comodules over a Hopf algebra H. If H is a group Hopf algebra, we study a more general Frobenius type property, uncover the structure of graded Frobenius algebras, and investigate graded symmetric algebras. The graded Frobenius concept is related to Frobenius functors.

[1]  S. Sehgal,et al.  Group Gradings on Associative Algebras , 2001 .

[2]  From subfactors to categories and topology. I. Frobenius algebras in and Morita equivalence of tensor categories , 2001, math/0111204.

[3]  Ross Street,et al.  Frobenius monads and pseudomonoids , 2004 .

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

[5]  Stefaan Caenepeel,et al.  Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations , 2002 .

[6]  Jurgen Fuchs,et al.  On Frobenius algebras in rigid monoidal categories , 2009, 0901.4886.

[7]  J. Fuchs,et al.  MODULAR INVARIANT FROBENIUS ALGEBRAS FROM RIBBON HOPF ALGEBRA AUTOMORPHISMS , 2011, 1106.0210.

[8]  C. Menini,et al.  When are induction and conduction functors isomorphic , 1994 .

[9]  S. Yamagami.  Frobenius Algebras in Tensor Categories and Bimodule Extensions , 2003 .

[10]  B. Torrecillas,et al.  On Frobenius and separable algebra extensions in monoidal categories. Applications to wreaths , 2013, 1303.0802.

[11]  C. Nastasescu,et al.  Methods of Graded Rings , 2004 .

[12]  Lowell Abrams.  Modules, Comodules, and Cotensor Products over Frobenius Algebras , 1998 .

[13]  Susan Montgomery,et al.  Hopf algebras and their actions on rings , 1993 .

[14]  Jeffrey Bergen.  A note on smash products over frobenius algebras , 1993 .

[15]  Lowell Abrams.  TWO-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORIES AND FROBENIUS ALGEBRAS , 1996 .

[16]  S. Raianu,et al.  Hopf algebras : an introduction , 2001 .

[17]  Tsit Yuen Lam,et al.  A first course in noncommutative rings , 2002 .

[18]  Tsit Yuen Lam,et al.  Lectures on modules and rings , 1998 .