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Journal of Lie Theory 23 (2013), No. 1, 143--158
Copyright Heldermann Verlag 2013

Algebraic Supergroups with Lie Superalgebras of Classical Type

Rita Fioresi
Dip. di Matematica, UniversitÓ di Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy

Fabio Gavarini
Dip. di Matematica, UniversitÓ di Roma "Tor Vergata", Via della ricerca scientifica 1, 00133 Roma, Italy

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 was defined and constructed explicitly by R. Fioresi and F. Gavarini [Chevalley Supergroups, Memoirs of the Amer. Math. Soc. 215 (2012), no. 1014].

Keywords: Algebraic supergroups, Lie superalgebras.

MSC: 14M30, 14A22; 58A50, 17B50

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