The purpose of this paper is to introduce and study weak Hom-bialgebras and weak Hom-Hopf algebras.
We provide relevant definitions, properties and constructions by twisting. Moreover, we extend to these classes of algebras, Kaplansky's procedure to construct weak Hom-bialgebras and weak Hom-Hopf algebras starting from any Hom-associative algebra and Hom-bialgebra.
Key Words: Hom-associative algebra, Weak Hom-bialgebra, weak Hom-Hopf algebra
2010 Mathematics Subject Classification: Primary 16T10. Secondary 16W10
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