**Memoirs of the American Mathematical Society**

2011;
64 pp;
Softcover

MSC: Primary 14;
Secondary 58; 17

Print ISBN: 978-0-8218-5300-9

Product Code: MEMO/215/1014

List Price: $60.00

Individual Member Price: $36.00

**Electronic ISBN: 978-0-8218-8521-5
Product Code: MEMO/215/1014.E**

List Price: $60.00

Individual Member Price: $36.00

# Chevalley Supergroups

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*Rita Fioresi; Fabio Gavarini*

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

# Table of Contents

## Chevalley Supergroups

- Chapter 1. Introduction 18 free
- Acknowledgements 411 free

- Chapter 2. Preliminaries 512
- Chapter 3. Chevalley bases and Chevalley algebras 1522
- Chapter 4. Kostant superalgebras 2532
- Chapter 5. Chevalley supergroups 3340
- Chapter 6. The cases A(1,1) , P(3) and Q(n) 5158
- Appendix A. Sheafification 5966
- Bibliography 6370