CBMS Regional Conference Series in Mathematics 1987; 80 pp; softcover Number: 69 Reprint/Revision History: reprinted 2000 ISBN10: 0821807196 ISBN13: 9780821807194 List Price: US$26 Member Price: US$20.80 All Individuals: US$20.80 Order Code: CBMS/69
 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 positivelysigned and negativelysigned 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 skewsymmetric 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  The superalgebra super \([A]\)
 Laplace pairings
 The standard basis theorem
 Invariant theory
 Examples
