Memoirs of the American Mathematical Society 2011; 64 pp; softcover Volume: 215 ISBN10: 0821853007 ISBN13: 9780821853009 List Price: US$60 Individual Members: US$36 Institutional Members: US$48 Order Code: MEMO/215/1014
 In the framework of algebraic supergeometry, the authors give a construction of the schemetheoretic supergeometric analogue of split reductive algebraic groupschemes, 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 schemetheoretic 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 PBWlike 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
