Chevalley Supergroups

By Rita Fioresi, F. Gavarini. 2008

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In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of split reductive algebraic group-schemes, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In particular, all Lie superalgebras of both basic and strange types are considered. This provides a unified approach to most of the algebraic supergroups considered so far in literature, and an effective method to construct new ones. Our method follows the pattern of a suitable scheme-theoretic revisitation of Chevalley’s construction of semisimple algebraic groups, adapted to the reductive case. 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5002083038c599a63b1206bdea223ce094555c33