Computers in Nonassociative Rings and Algebras

Computers in Nonassociative Rings and Algebras

1st Edition - January 1, 1977

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  • Editors: Robert E. Beck, Bernard Kolman
  • eBook ISBN: 9781483267951

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Description

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.

Table of Contents


  • 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

Product details

  • No. of pages: 308
  • Language: English
  • Copyright: © Academic Press 1977
  • Published: January 1, 1977
  • Imprint: Academic Press
  • eBook ISBN: 9781483267951

About the Editors

Robert E. Beck

Bernard Kolman

Affiliations and Expertise

Drexel University

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