Chevalley Supergroups

Abstract

In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In particular both basic (even exceptional) and strange cases are covered. This provides a unified approach to most of the algebraic supergroups considered so far in literature, and an effective method to construct new ones. As an intermediate step, we prove an existence theorem for Chevalley bases of simple classical Lie superalgebras and a PBW-like theorem for their associated Kostant superalgebras.

La-TeX file, 95 pages. New version revised after correcting the journal's galley proofs. Some key corrections are in pages 31, 32 and 34, concerning the given explicit examples of Chevalley basis in cases B, C, D and P

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Cited by in corpus (20)

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• \vS{a}povalov elements and the Jantzen sum formula for contragredient Lie superalgebras
• SUSY structures, representations and Peter-Weyl theorem for $S^{1|1}$
• Finite $W$-superalgebras and the dimensional lower bounds for the representations of basic Lie superalgebras
• Affine algebraic super-groups with integral
• The Projective Linear Supergroup and the SUSY-preserving automorphisms of ${\mathbf{P}}^{1|1}$
• Finite W-superalgebras for basic Lie superalgebras
• Finite W-superalgebras for basic classical Lie superalgebras
• Frobenius kernels of algebraic supergroups and Steinberg's tensor product theorem
• Algebraic supergroups and Harish-Chandra pairs over a commutative ring
• SUSY $N$-supergroups and their real forms
• Modular representations of exceptional supergroups
• Centers of universal enveloping algebras of Lie superalgebras in prime characteristic
• Compact forms of Complex Lie Supergroups
• Singular Degenerations of Lie Supergroups of Type $D(2,1;a)$
• Highest weight Harish-Chandra supermodules and their geometric realizations