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Chevalley Supergroups

R. Fioresi Università di Bologna, Bologna, Italy
F. Gavarini Università di Roma "Tor Vergata", Rome, Italy
Available Formats:
Electronic ISBN: 978-0-8218-8521-5
Product Code: MEMO/215/1014.E
List Price: $60.00 MAA Member Price:$54.00
AMS Member Price: $36.00 Click above image for expanded view Chevalley Supergroups R. Fioresi Università di Bologna, Bologna, Italy F. Gavarini Università di Roma "Tor Vergata", Rome, Italy Available Formats:  Electronic ISBN: 978-0-8218-8521-5 Product Code: MEMO/215/1014.E  List Price:$60.00 MAA Member Price: $54.00 AMS Member Price:$36.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 2152011; 64 pp
MSC: Primary 14; Secondary 58; 17;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Chevalley bases and Chevalley algebras
• 4. Kostant superalgebras
• 5. Chevalley supergroups
• 6. The cases $A(1,1) \,$, $P(3)$ and $Q(n)$
• A. Sheafification
• Requests

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Volume: 2152011; 64 pp
MSC: Primary 14; Secondary 58; 17;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Chevalley bases and Chevalley algebras
• 4. Kostant superalgebras
• 5. Chevalley supergroups
• 6. The cases $A(1,1) \,$, $P(3)$ and $Q(n)$
• A. Sheafification
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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