**CBMS Regional Conference Series in Mathematics**

Volume: 69;
1987;
80 pp;
Softcover

MSC: Primary 15;
Secondary 05; 11; 16; 17

Print ISBN: 978-0-8218-0719-4

Product Code: CBMS/69

List Price: $28.00

Individual Price: $22.40

**Electronic ISBN: 978-1-4704-2429-9
Product Code: CBMS/69.E**

List Price: $28.00

Individual Price: $22.40

# Invariant Theory and Superalgebras

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*Frank D. Grosshans; Gian-Carlo Rota; Joel A. Stein*

A co-publication of the AMS and CBMS

This book brings the reader to the frontiers of research in some topics in superalgebras and symbolic method in invariant theory. Superalgebras are algebras containing positively-signed and negatively-signed variables. One of the book's major results is an extension of the standard basis theorem to superalgebras. This extension requires a rethinking of some basic concepts of linear algebra, such as matrices and coordinate systems, and may lead to an extension of the entire apparatus of linear algebra to “signed” modules. The authors also present the symbolic method for the invariant theory of symmetric and of skew-symmetric tensors. In both cases, the invariants are obtained from the symbolic representation by applying what the authors call the umbral operator. This operator can be used to systematically develop anticommutative analogs of concepts of algebraic geometry, and such results may ultimately turn out to be the main byproduct of this investigation.

While it will be of special interest to mathematicians and physicists doing research in superalgebras, invariant theory, straightening algorithms, Young bitableaux, and Grassmann's calculus of extension, the book starts from basic principles and should therefore be accessible to those who have completed the standard graduate level courses in algebra and/or combinatorics.

#### Table of Contents

# Table of Contents

## Invariant Theory and Superalgebras

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Introduction v6 free
- Synopsis vii8 free
- Notation Guide xxi22 free
- Chapter 1. The Superalgebra Super[A] 126 free
- Chapter 2. Laplace Pairings 1338
- Chapter 3. The Standard Basis Theorem 2550
- Chapter 4. Invariant Theory 4166
- Chapter 5. Examples 5580
- References 75100
- Index 79104
- Back Cover Back Cover1106