Abstract
ABSTRACTWe define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of affine group schemes and are in correspondence with graded Hopf algebras. Graded group varieties take the place of infinitesimal group schemes. We generalize the result that connected graded bialgebras are graded Hopf algebra to our setting and we describe the algebra structure of graded group varieties. We relate these new objects to the classical ones providing a new and broader framework for the study of graded Hopf algebras and affine group schemes.
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