Q-graded Hopf quasigroups
Abstract
Firstly, we introduce a class of new algebraic systems which generalize Hopf quasigroups and Hopf π-algebras called Q-graded Hopf quasigroups, and research some properties of them. Secondly, we define the representations of Q-graded Hopf quasigroups, i.e Q-graded Hopf quasimodules, research the construction method and fundamental theorem of them. Thirdly, we research the smash products of Q-graded Hopf quasigroups.
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