Algebraic supergroups with lie superalgebras of classical type

摘要

We show that every connected affine algebraic supergroup defined over a field k, with diagonalizable maximal torus and whose tangent Lie superalgebra is a k-form of a complex simple Lie superalgebra of classical type is a Chevalley supergroup, as it is defined and constructed explicitly in [R. Fioresi, F. Gavarini, Chevalley Supergroups, Memoirs of the Amer. Math. Soc. 215 (2012), no. 1014].