The classical Yang-Baxter equation on alternative algebras: the alternative -bialgebra structure on Cayley-Dickson matrix algebras.
The elliptic dynamical quantum group as an -Hopf algebroid.
The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules
We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category . More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke’s theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.