Chevalley Supergroups of type D(2,1;a)
Abstract
I present a construction "a` la Chevalley" of affine supergroups associated with simple Lie superalgebras of (classical) type D(2,1;a), for any possible value of the parameter a - in particular, including non-integral values of a. This extends the similar work performed in [R. Fioresi, F. Gavarini, "Chevalley Supergroups", Memoirs of the AMS 215 (2012), no. 1014 - arXiv:0808.0785v8 [math.RA]], where all other simple Lie superalgebras of classical type were considered. The case of simple Lie superalgebras of Cartan type is dealt with in [F. Gavarini, "Algebraic supergroups of Cartan type", Forum Mathematicum (to appear), 92 pages - arXiv:1109.0626v5 [math.RA], so this work completes the program of constructing connected affine supergroups associated with any simple Lie superalgebra.
Keywords
Cite
@article{arxiv.1006.0464,
title = {Chevalley Supergroups of type D(2,1;a)},
author = {Fabio Gavarini},
journal= {arXiv preprint arXiv:1006.0464},
year = {2012}
}
Comments
La-TeX file, 20 pages. All the text was amended after the referee's remarks. To appear in "Proceedings of the Edinburgh Mathematical Society"