Computers in nonassociative rings and algebras : special session on computers in the study of nonassociative rings and algebras at the 82nd Annual Meeting of the American Mathematical Society ; San Antonio, January 22-26, 1976

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. Content: Front Matter, Page iii Copyright, Page iv List of Contributors, Pages vii-viii Preface, Page ix EXAMPLES, COUNTEREXAMPLES AND THE COMPUTER, Pages 1-12, Erwin Kleinfeld PROCESSING IDENTITIES BY GROUP REPRESENTATION, Pages 13-40, Irvin Roy Hentzel AN UNNATURAL ATTACK ON THE STRUCTURE PROBLEM FOR THE FREE JORDAN RING ON 3 LETTERS: AN APPLICATION OF QUAD ARITHMETIC, Pages 41-138, B.T. Smith, L.T. Wos ON THE INVARIANTS OF A LIE GROUP. I, Pages 139-155, Hans Zassenhaus COMPUTATION OF CASIMIR INVARIANTS OF LIE ALGEBRAS, Pages 157-165, C.W. Conatser, P.L. Huddleston COMPUTING THE STRUCTURE OF A LIE ALGEBRA, Pages 167-188, Robert E. Beck, Bernard Kolman, Ian N. Stewart WHAT IS THE TYPICAL NILPOTENT LIE ALGEBRA?, Pages 189-207, Eugene M. Luks INTEGER CLEBSCH-GORDAN COEFFICIENTS FOR LIE ALGEBRA REPRESENTATIONS, Pages 209-234, Johan G.F. Belinfante THE COMPUTATION OF BRANCHING RULES FOR REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS, Pages 235-277, W. McKay, J. Patera, D. Sankoff SYMMETRIZED KRONECKER POWERS OF REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS, Pages 279-293, Nigel Backhouse Index, Pages 295-297 Edited By Robert E. Beck, Bernard Kolman. An Outgrowth Of The Special Session On Computers In The Study Of Nonassociative Rings And Algebras ... Held At The 82nd Annual Meeting Of The American Mathematical Society In San Antonio, January 22-26, 1976. Includes Bibliographies And Index.