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Let  L  be an  n -dimensional null-filiform Leibniz algebra over a field  K . We consider a finite dimensional cocommutative Hopf algebra or a Taft algebra  H  and we describe the  H -actions on  L . Moreover we provide the set of  H -identities and the description of the  S   n  -module structure of the relatively free algebra of  L .

Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras