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The dual category with respect to the category of differential groups is defined and investigated. The objects of this category are algebras, called Hopf–Sikorski (H-S) algebras, the axioms of which combine the axioms of Sikorski’s algebras with modified axiomas of Hopf algebras. Morphisms of this category are structural mappings corresponding to Hopf algebras that are smooth in the sense of Sikorski. As an example, we discuss the H-S algebra of the Lorentz group.

Hopf–Sikorski algebras