E-Book, Englisch, 308 Seiten, Web PDF
Beck / Kolman Computers in Nonassociative Rings and Algebras
1. Auflage 2014
ISBN: 978-1-4832-6795-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 308 Seiten, Web PDF
ISBN: 978-1-4832-6795-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Computers in Nonassociative Rings and Algebras;4
3;Copyright Page;5
4;Table of Contents;6
5;List of Contributors;8
6;Preface;10
7;CHAPTER 1. EXAMPLES, COUNTEREXAMPLES AND THE COMPUTER;12
7.1;References;20
8;CHAPTER 2. PROCESSING IDENTITIES BY GROUP REPRESENTATION;24
8.1;1. Introduction;24
8.2;2. Theory;25
8.3;3. Identities Involving Several Functions;26
8.4;4. Identities Modulo An Additive Subgroup;27
8.5;5. Applications;28
8.6;6. Representation;43
8.7;7. Orientation to a Computer;49
8.8;8. Problems;49
8.9;Acknowledgement;50
8.10;References;50
9;CHAPTER 3. AN UNNATURAL ATTACK ON THE STRUCTURE PROBLEM FOR THE FREE JORDAN RING ON 3 LETTERS: AN APPLICATION OF QUAD ARITHMETIC;52
9.1;Abstract;52
9.2;1. Introduction;53
9.3;2. Problem Specification, Closing Functions, and the Data Structure;57
9.4;3. The Basic Algorithms;100
9.5;4. Closing Functions: The Formal Presentation;117
9.6;5. Quad Arithmetic and the Identity E;129
9.7;6. Dimension, the Kernel, Conjectures, and Open Questions;136
9.8;Acknowledgments;149
9.9;References;149
10;CHAPTER 4. ON THE INVARIANTS OF A LIE GROUP. I;150
10.1;1;150
10.2;2. In modern terminology the Casimir
operator;151
10.3;3;153
10.4;4;155
10.5;5;158
10.6;6;159
10.7;7. We observe that the
mapping;160
10.8;8;161
10.9;9;164
10.10;10. In
terms of the preceding definitions the following answers were found;165
10.11;References;166
11;CHAPTER 5. COMPUTATION OF CASIMIR INVARIANTS OF LIE ALGEBRAS;168
11.1;1. Introduction;168
11.2;2. The System of Equations For Casimir Invariants of Degree d;169
11.3;3. The Systems of Equations for Degrees One, Two,
and Three;172
11.4;4. Algorithms and Their Implementation;173
11.5;5. Concluding Remarks;174
11.6;References;175
12;CHAPTER 6. COMPUTING THE STRUCTURE OF A LIE ALGEBRA;178
12.1;1. Introduction;178
12.2;2. Linear Algebra;180
12.3;3. Fundamental Lie Algebra Properties;181
12.4;4. Series;186
12.5;5. The Soluble Radical;188
12.6;6. The Nil Radical;188
12.7;7. Construction of a Non-Nilpotent Element;191
12.8;8. The Cartan Subalgebra;193
12.9;9. An Example;196
12.10;Acknowledgement;198
12.11;References;198
13;CHAPTER 7. WHAT IS THE TYPICAL NILPOTENT LIE ALGEBRA?;200
13.1;1. Introduction;200
13.2;2. Notations and Preliminaries;201
13.3;3. Metabelian Lie Algebras;202
13.4;4. Nilpotent Lie Algebras;209
13.5;Acknowledgment;217
13.6;References;218
14;CHAPTER 8. INTEGER CLEBSCH-GORDAN COEFFICIENTS FOR LIE ALGEBRA REPRESENTATIONS;220
14.1;1. Introduction;220
14.2;2. Classical Work, Before 1960;221
14.3;3. Work in the 1960's;226
14.4;4. Recent Work, Since 1970;236
14.5;5. Outlook;241
14.6;Bibliography (arranged in chronological order);241
15;CHAPTER 9. THE COMPUTATION OF BRANCHING RULES FOR REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS;246
15.1;1. Introduction;246
15.2;2. Method;247
15.3;3. The Program;254
15.4;4. Examples;259
15.5;References;265
16;CHAPTER 10. SYMMETRIZED KRONECKER POWERS OF REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS;290
16.1;1. Introduction;290
16.2;2. The Frobenius Formula and Its Applications;291
16.3;3. The Algebra A2;294
16.4;4. The Algebra B2 (C2);299
16.5;5. The Algebra .1 x .1;300
16.6;6. Conclusion;301
16.7;Acknowledgement;302
16.8;References;302
17;Index;306
