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.
Keywords
Cite
@article{arxiv.0808.0785,
title = {Chevalley Supergroups},
author = {R. Fioresi and F. Gavarini},
journal= {arXiv preprint arXiv:0808.0785},
year = {2012}
}
Comments
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