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Invariant Theory and Superalgebras
 
A co-publication of the AMS and CBMS
Invariant Theory and Superalgebras
Softcover ISBN:  978-0-8218-0719-4
Product Code:  CBMS/69
List Price: $32.00
Individual Price: $25.60
eBook ISBN:  978-1-4704-2429-9
Product Code:  CBMS/69.E
List Price: $30.00
Individual Price: $24.00
Softcover ISBN:  978-0-8218-0719-4
eBook: ISBN:  978-1-4704-2429-9
Product Code:  CBMS/69.B
List Price: $62.00 $47.00
Invariant Theory and Superalgebras
Click above image for expanded view
Invariant Theory and Superalgebras
A co-publication of the AMS and CBMS
Softcover ISBN:  978-0-8218-0719-4
Product Code:  CBMS/69
List Price: $32.00
Individual Price: $25.60
eBook ISBN:  978-1-4704-2429-9
Product Code:  CBMS/69.E
List Price: $30.00
Individual Price: $24.00
Softcover ISBN:  978-0-8218-0719-4
eBook ISBN:  978-1-4704-2429-9
Product Code:  CBMS/69.B
List Price: $62.00 $47.00
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 691987; 80 pp
    MSC: Primary 15; Secondary 05; 11; 16; 17

    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.

    Readership

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. The Superalgebra $\text {Super}[A]$
    • Chapter 2. Laplace Pairings
    • Chapter 3. The Standard Basis Theorem
    • Chapter 4. Invariant Theory
    • Chapter 5. Examples
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 691987; 80 pp
MSC: Primary 15; Secondary 05; 11; 16; 17

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.

Readership

  • Chapters
  • Chapter 1. The Superalgebra $\text {Super}[A]$
  • Chapter 2. Laplace Pairings
  • Chapter 3. The Standard Basis Theorem
  • Chapter 4. Invariant Theory
  • Chapter 5. Examples
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.