Computers in Nonassociative Rings and Algebras

Computers in Nonassociative Rings and Algebras provides information pertinent to the computational aspects of nonassociative rings and algebras. This book describes the algorithmic approaches for solving problems using a computer.

Organized into 10 chapters, this book begins with an overview of the concept of a symmetrized power of a group representation. This text then presents data structures and other computational methods that may be useful in the field of computational algebra. Other chapters consider several mathematical ideas, including identity processing in nonassociative algebras, structure theory of Lie algebra, and representation theory. This book presents as well an historical survey of the use of computers in Lie algebra theory, with specific reference to computing the coupling and recoupling coefficients for the irreducible representations of simple Lie algebras. The final chapter deals with how representations of semi-simple Lie algebras can be symmetrized in a straightforward manner.

This book is a valuable resource for mathematicians.

List of Contributors

Preface

Examples, Counterexamples and the Computer

Processing Identities by Group Representation

An Unnatural Attack on the Structure Problem for the Free Jordan Ring on 3 Letters: An Application of Quad Arithmetic

On the Invariants of a Lie Group.I

Computation of Casimir Invariants of Lie Algebras

Computing the Structure of a Lie Algebra

What is the Typical Nilpotent Lie Algebra?

Integer Clebsch-Gordon Coefficients for Lie Algebra Representations

The Computation of Branching Rules for Representations of Semisimple Lie Algebras

Symmetrized Kronecker Powers of Representations of Semisimple Lie Algebras

Index