The structure and construction of bi-Frobenius Hom-algebras

Equivalent crossed products of monoidal Hom-Hopf algebras

“…Consequently, the antipodes, integrals and Drinfel'd doubles of Hom-Hopf algebras were considered in [6,16]. Further, some modules and comodules on these Hom-algebras structures such as Hom-module algebras, Hom-comodule algebras and Hom-Hopf modules were considered in [5,4,3,19].…”

Hom-Yang-Baxter Equations and Frobenius Monoidal Hom-Algebras

“…The concept of Frobenius algebras is very important because of the connections to such diverse areas as group representations, homology of a compact oriented manifold, topological quantum field theories, quantum cohomology, Gorenstein rings in commutative algebras, Hopf algebras, coding theory, Lie quasi-Frobenius algebras, and the classical (quantum) Yang-Baxter equation (see [18][19][20][21]). In addition, there is a "quantum version" of the classical result that any finite dimensional Hopf algebra is Frobenius.…”