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Chevalley Supergroups
R. Fioresi, Università di Bologna, Italy, and F. Gavarini, Università di Roma "Tor Vergata", Rome, Italy
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Memoirs of the American Mathematical Society
2011; 64 pp; softcover
Volume: 215
ISBN-10: 0-8218-5300-7
ISBN-13: 978-0-8218-5300-9
List Price: US$60
Individual Members: US$36
Institutional Members: US$48
Order Code: MEMO/215/1014
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In the framework of algebraic supergeometry, the authors 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 the literature, and an effective method to construct new ones.

The authors' 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, they prove an existence theorem for Chevalley bases of simple classical Lie superalgebras and a PBW-like theorem for their associated Kostant superalgebras.

Table of Contents

  • Introduction
  • Preliminaries
  • Chevalley bases and Chevalley algebras
  • Kostant superalgebras
  • Chevalley supergroups
  • The cases \(A(1,1)\), \(P(3)\) and \(Q(n)\)
  • Appendix A. Sheafification
  • Bibliography
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