On Coverings and Hyperalgebras of Affine Algebraic Groups, III
Copyright policy )On Coverings and Hyperalgebras of Affine Algebraic Groups, III
Over an algebraically closed field of characteristic zero, the universal group covering of a connected affine algebraic group, if such exists, can be constructed canonically from its Lie algebra only. In particular the isomorphism classes of simply connected affine algebraic groups are in 1-1 correspondence with the isomorphism classes of finite dimensional Lie algebras of some sort. We shall consider the counterpart of these results (due to Hochschild) in case of a positive characteristic, replacing the Lie algebra by the “hyperalgebra". We show that the universal group covering of a connected affine algebraic group scheme can be constructed canonically from its hyperalgebra only and hence, in particular, that the category of simply connected affine algebraic group schemes is equivalent to a subcategory of the category of hyperalgebras of finite type which contains all the semisimple hyperalgebras.
- University of Tsukuba Japan
Group schemes, hyperalgebra, Coverings in algebraic geometry, Hopf algebra, Linear algebraic groups over arbitrary fields, Hopf algebras (associative rings and algebras), Affine algebraic groups, hyperalgebra constructions, pro-affine algebraic group, Lie algebras of linear algebraic groups, Linear algebraic groups over adèles and other rings and schemes, universal group covering
Group schemes, hyperalgebra, Coverings in algebraic geometry, Hopf algebra, Linear algebraic groups over arbitrary fields, Hopf algebras (associative rings and algebras), Affine algebraic groups, hyperalgebra constructions, pro-affine algebraic group, Lie algebras of linear algebraic groups, Linear algebraic groups over adèles and other rings and schemes, universal group covering
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